Spurious Pulse Detection in Fibre-Optic Channels Using Measurement-Device-Independent Quantum Key Distribution with Single-Photon Avalanche Photodiodes

Spurious Pulse Detection in Fibre-Optic Channels Using Measurement-Device-Independent Quantum Key Distribution with Single-Photon Avalanche Photodiodes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Spurious Pulse Detection in Fibre-Optic Channels Using Measurement-Device-Independent Quantum Key Distribution with Single-Photon Avalanche Photodiodes Suneetha J, Smitha Darandale This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8711394/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The safe exchange of cryptographic keys is made possible by Quantum Key Distribution (QKD), which makes use of the basic ideas of quantum physics. Quantum Bit Error Rate (QBER), key generation rate, and transmission distance are important performance measures in QKD systems. Nevertheless, undesired noise sources that impair system performance, such dark counts and afterpulses, restrict traditional QKD implementations. The Measurement-Device-Independent QKD (MDI-QKD) protocol and Single Photon Avalanche Diodes (SPADs) for single-photon detection are combined in this research to create an improved QKD model. All detector-side-channel weaknesses are naturally eliminated by the MDI-QKD protocol, while SPADs' excellent sensitivity and temporal precision allow for precise noise source detection and characterisation, including dark count and afterpulse rates. When compared to conventional QKD systems, the suggested method performs better when assessed using QBER. According to experimental findings, including SPADs into the MDI-QKD architecture greatly improves the security and effectiveness of quantum communication systems by detecting detector-induced errors. Measure Device Independent Quantum key distribution protocol (MDI-QKD) Single Photon Avalanche diode (SPAD) Dark count Rate (DCR) After pulse Rate (APR) Quantum bit error rate (QBER) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 INTRODUCTION In view of the widespread usage of information systems in many facets of everyday life, there are many information security issues, and security threats are become more prevalent and intricate. Academics and business are becoming increasingly concerned about the security of personal data sent via the Internet. However, because of their greater processing capacity, the advent of quantum computers poses a serious threat to conventional cryptosystems. To create an encrypted connection between two users, a secret communication protocol employs a number of traditional public key cryptography [ 1 ] primitives. One important area of quantum information science is quantum cryptography (QC) [ 2 ], often known as quantum key distribution. Providing a totally secure data transfer between two parties—typically referred to as Alice (Sender) and Bob (Receiver)—is the main goal of quality control. While current encryption systems rely on mathematical laws, rendering transmitted messages potentially vulnerable to decoding, the underlying principles of quantum physics provide security and invulnerability to eavesdropping. According to the Shannon theory, if a transmission is encrypted using a random one-time key whose length corresponds to the message, it might not be decoded since only authorized users are aware of the key. The primary challenge in executing this strategy is the distribution of a secret quantum key among distant users. The photo photoelectric effect, in which photons transmit their energy to electrons in a substance and cause the electrons to be released, is the basis for how a single photon detector (SPD) operates. This phenomena is used by SPD to identify individual photons. The single-photon detector for incorrect pulses on the receiver's end is a problem in Quantum Key Distribution (QKD) [ 3 ]. The method used to detect single photons is the single-photon avalanche diode in linear mode [ 4 ]. A cutting-edge security method for sending safe keys is called Quantum Key Distribution (QKD). The foundation of this key distribution technique is quantum physics. Both the sender and the recipient of a secure message may identify efforts at eavesdropping thanks to QKD [ 5 ]. In quantum physics, the discovery of eavesdropping within the quantum channel is guaranteed by Heisenberg's uncertainty principle. Furthermore, an eavesdropper cannot produce unexpected quantum states or replicate additional qubits. The two transmitting and receiving components of the QKD system are situated on opposing sides of the quantum channel. Highly sensitive data, including genetic, pharmacological, and personal medical records, is managed via a permanent secure storage network that uses QKD, secret sharing, and authentication methods. The increasing concern over data privacy suggests that this storage network may become a vital application of QKD. LITERATURE SURVEY In their paper, Akram Youssry et al. [ 8 ] provide a novel technique for noise detection that combines quantum feature synthesis techniques with spectator qubits. The method consists of a two-phase protocol: an execution phase where real-time measurements of the spectator qubit offer information for the best control pulses sent to the data qubit, and a characterisation phase where a machine learning-based grey box model specifies noise profiles. This technique enhances qubit fidelity and aids in differentiating various noise patterns. However, this study's dependence on labeled characterisation data, which can be challenging to get in real-world circumstances, is a significant restriction. Furthermore, in dynamic quantum settings, the assumption that the noise influencing the spectator and data qubits is constant throughout time could not be true. The integrity of a two-state quantum bit commitment mechanism under realistic noise conditions is investigated by Ricardo Loura et al. [ 9 ]. The authors use a combination of depolarizing channels, unitary development, and basis-dependent channels to describe errors caused by background noise and equipment defects, including sources, fibers, and detectors. The method makes use of information-theoretic criteria, such as fidelity and relative entropy, to evaluate the impact of noise and offer the best ways to cheat. The majority of the work is theoretical, and the proposed models might not accurately capture the complexities of practical implementations. Furthermore, although discussing noisy and confined quantum memory, the article's applicability to actual quantum communication systems is limited due to its lack of empirical support. The effectiveness of Single-Photon Avalanche Diodes (SPADs) in time-gated photon-counting applications is examined by Mahmoudi et al. [ 10 ]. Delineating noise sources and failure mechanisms in SPAD detectors is likely the focus of the effort, which is crucial for applications that need precise photon detection. To evaluate SPAD performance under various conditions, experimental measurements are used to look at factors including jitter, after pulsing, and dark count rate. This research's dependence on specific SPAD designs, which could not be applicable to numerous models, is a major limitation. Furthermore, SPAD performance may be impacted by external factors like temperature fluctuations and electromagnetic interference, which may not be fully taken into account during the characterization process. A technique for evaluating important SPAD characteristics, such as detection efficiency, dark count rate, timing jitter, and after-pulsing phenomena, was proposed by Rahmanpour et al. [ 11 ]. The procedure most likely involves controlled experimental setups where SPADs are exposed to certain light sources and their responses are measured using statistical analysis and time-correlated single-photon counting. The quality of the experimental equipment and the calibration of measuring devices have a major impact on the accuracy of these characterization techniques. Errors might be caused by external factors like temperature changes and ambient light, and the need for specialist equipment might make these processes inaccessible to all research institutes. The significance of security flaws in Quantum Key Distribution (QKD) systems caused by correlated intensity fluctuations in optical pulses is emphasized by Yoshino et al. [ 12 ]. Presumably, the study offers a real-time pulse intensity monitoring and stabilization method or a protocol modification that reduces vulnerability to such fluctuations. The effectiveness of this countermeasure, which shows improvements in security and key generation rates under varied conditions, is evaluated by theoretical analysis and perhaps experimental validation. However, implementing such a countermeasure could be more difficult, requiring sophisticated hardware and signal processing techniques. Depending on the precise features of the intensity changes, trade-offs between increased security and system performance may occur, possibly leading to larger delays or lower key generation rates. Furthermore, although the countermeasure may mitigate one attack vector, additional potential vulnerabilities in QKD systems persist unexplored. According to Liu et al. [ 13 ], Quantum Key Agreement (QKA) has become a crucial cryptographic foundation, enabling secure multi-party key production that outperforms conventional methods. However, traditional QKA protocols have security vulnerabilities, particularly to detector-side-channel attacks that attackers might exploit. Measurement-Device-Independent (MDI) QKA methods have been put in place to reduce these risks by eliminating reliance on reliable measurement tools. By using post-selected Greenberger-Horne-Zeilinger (GHZ) states, the proposed MDI-QKA protocol enhances security by ensuring participant fairness and prevents any subset from independently determining the key. By assuming that just the state preparation devices are reliable, this method improves resilience against eavesdropping in comparison to previous MDI-QKA protocols. Notwithstanding these gains, efficiency concerns remain, particularly with an increasing number of participants, demanding further study on optimizing critical production rates and mitigating noise-related issues for practical application. This paper includes This study presents an innovative modelling framework for MDI-QKD that integrates real-world defects of Single Photon Avalanche Diodes (SPAD), including dark count rate, after pulsing, and dead time. In contrast to idealized simulations, the simulation accurately reflects the influence of detector-level noise sources throughout a 1000 km fibre-optic link, offering a realistic performance assessment. A comparative study between optimal and noisy systems reveals the deterioration in QBER and key length, providing essential insights for the development of realistic quantum communication systems. METHODOLOGIES 3.1 Quantum key distribution Delivering individual photons, each encoded with a random quantum state, via fiber-optic channels between communication parties is how QKD [ 14 ] works. As a series of qubits, these quantum states represent binary values and serve as the quantum equivalent of classical bits. Each photon interacts with a beam splitter upon arrival, which randomly directs it to one of two receptors. Using a classical channel, the receiver records the measurement data and communicates to the sender the fundamental decisions made for measurement. In order to identify similar events, the sender then compares these with the original preparation foundation. Measurements that are inconsistent or unclear are removed; only photon measurements when the preparation and measuring bases match are kept. The resultant shared bit sequence, referred to as the sifting key, can then be utilized for safe data encryption. QKD protocols are performed in five stages [ 14 , 19 ] 1. Qubit preparation transmission · At this stage, the sender prepares quantum states (qubits) on a selected basis, such as the rectilinear (∣0⟩, ∣1⟩) or diagonal (∣+⟩, ∣−⟩) basis. · The quantum bits are then sent to the recipient via a quantum channel, usually via a fibre optic or free-space connection. · During transmission, quantum states may be influenced by noise and any eavesdropping efforts. 2. Shifting · The receiver randomly assesses the received qubits utilizing one of the two available bases. · After measurement, Sender and Receiver engage in classical communication to compare the bases utilized for each qubit, without disclosing the actual bit values. · They save just the measurements where each utilized the identical foundation, so creating a mutual filtered key. 3. Parameter estimation · Sender and Receiver publicly compare a portion of their filtered key to identify the existence of an eavesdropper (Eve). · They compute the QBER, which quantifies differences among their key bits. · Should the mistake rate be above a certain threshold, they infer the existence of eavesdropping and invalidate the key. Alternatively, they advance to the subsequent stage. 4. Post processing · Correction of mistakes: Due to the possibility of introduction of mistakes by noise or mild disruptions, both Sender and Receiver employ conventional error correction methods [6] (e.g., Cascade, Winnow) to resolve disparities. · Privacy Amplification: To eliminate whatever incomplete information that an eavesdropper may have acquired, Sender and Receiver utilize hash algorithms or compression methods to produce a concise, highly secure final key. 5. Authentication Sender and Receiver employ traditional cryptographic authentication [ 1 , 8 ], such as Message Authentication Codes, to safeguard against man-in-the-middle attacks and ensure the integrity of their communications. Upon authentication, the definitive secret key is prepared for the safe encryption of communications. Figure 2 provides about detailed explanation steps how the key between the sender and receiver. QKD is a fundamental basis in QC. In a QKD protocol, many untrusted parties can collaboratively establish a shared key, ensuring that each party has equal influence on the key and that no subset can independently determine it. Nonetheless, in real QKD, the flaws in the detectors of the participants can be used to undermine the security and integrity of QKD. A MDI- QKD protocol is suggested to eliminate all detector-side-channel vulnerabilities. 3.2 Measurement device independent protocol (MDI) MDI-QKD is a quantum cryptography technology created to mitigate and eradicate security risks stemming from flawed or untrusted measurement equipment. MDI-QKD procedure 1. Qubit Preparation: A and B independently generate weak coherent pulses (WCPs) utilizing randomly selected basis states (ZZ or XX) and intensity configurations. The probability for base selection is PZ Z-basis (1) PX = 1 – PZ X-basis. (2) Intensity settings (γs, γv, γw) are selected with probabilities ps, pv, pw, respectively. The intensities are refined for key generation and parameter estimation. 2. Qubit Encoding A and B encode random data into their generated WCPs utilizing an encoding strategy, such as polarization or phase encoding [ 14 , 20 ]. The encoded pulses are transmitted to an untrusted relay (e.g., Charlie C) using quantum channels. 3. Bell state Measurement (BSM) [ 20 ] The untrusted relay executes a BSM on the incoming pulses from A and B. Successful BSM outcomes demonstrate entanglement-like correlations between A's and B's states, utilized for key generation. C openly discloses the measurement findings while withholding any details on the encoded bits. 4. Qubit shifting A and B evaluate their base selections over a classical channel. Only data utilizing the identical base is preserved for subsequent processing. This stage eliminates incongruent basis data to maintain consistency in key generation. 5. Parameter Estimation Alice and Bob examine a portion of their retained data to assess mistake rates and identify possible eavesdropping. Decoy-state approaches are employed to precisely estimate the contribution of single-photon pulses, hence safeguarding against photon-number-splitting attackers. 6. Reconciliation A and B utilize conventional error correction techniques to align their raw keys into congruent shared keys. Discrepancies arising from noise or channel defects are rectified at this phase. 7. Privacy Amplification A and B [ 15 ] employ privacy amplification techniques to remove whatever incomplete knowledge that an eavesdropper may have acquired. This condenses the raw key into a more concise yet entirely secure final key. 3.3 Dark count rate The DCR [ 16 ] can be described as the number of pulses per second recorded in the absence of light, specifically measured without the presence of photons [ 17 , 21 ]. The inaccurate detection events mostly stem from heat sources and may thus be significantly mitigated by employing a cooled detector type. $$\:DCR=\frac{\text{N}\text{D}}{\text{D}\text{u}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}}$$ 3 Where ND is the summation of dark counts detected over a period of duration Duration is the measurement of time in seconds 3.4 After pulse rate The After Pulse Rate (APR) [ 16 ] is the proportion of observed events in a photon detector that lead to incorrect secondary detections caused by charge trapping and release delays [ 17 , 21 ]. It measures the likelihood that a dark count or a legitimate photon detection induces an extra false count. $$\:APR=\frac{\text{N}\text{A}}{\sum\:NT}$$ 4 Where NA is the number of after-pulse events detected NT is the total number of detected counts (including dark counts, after pulse, and single photons) 3.5 Quantum bit error rate [ 9 , 15 ] The QBER quantifies faults in a QKD system. It denotes the proportion of erroneous bits to the overall quantity of sent bits in the filtered key. QBER= \(\:\frac{NE}{\sum\:NS}\) (5) Where NE=number of erroneous bits in the shifted key NS=Total number of shifted key bits 3.6 SPAD In addition to their single-photon sensitivity, high detection efficiency, low dark count rates, and low timing jitter, Single Photon Avalanche Diodes (SPADs), particularly InGaAs/InP planar-geometry devices designed for the 1.55 µm telecommunications wavelength, are incredibly promising detectors for QKD [ 17 ]. To meet the strict requirements of QKD systems, the SPADs go through extensive modeling, manufacturing, and characterization. This allows for safe key distribution across long distances at reasonable key rates. Recent advances include GHz-gated InGaAs/InP single-photon avalanche diodes (SPADs) that are electrically cooled and achieve detection efficiency close to 6% and dark count probabilities as low as 2.8×10⁻². These developments have made it possible for fiber optics to achieve secure key speeds of 24 kbit/s across a 100-kilometer distance. The probability that an incoming photon is successfully detected photon detection probability PDP = QE*PP (6) Where QE=Quantum Efficiency PP=Photon probability Dark counts are false detections due to thermal or electronic noise: Dark count probability (DCP) DCP= \(\:1-{e}^{-DCR.T\:window}\) (7) Where DCR=Dark count Rate, counts per second Twindow =detection time window After pulse probability (APP) after pulsing occurs when a previously detected photon triggers a secondary false detection. The probability of APP APP = Ap*P (8) Where AP Probability of an after pulse per detection P=photon detected Total count probability TCP = PDP+DCP + APP (9) 3.7 Fibre optic channel Fiber optic communication is an optical communication method that uses visible or infrared light pulses to send data across an optical fiber. Light functions as an electromagnetic wave that has been altered to convey data [ 8 ]. When high bandwidth, long distances, or resistance to electromagnetic interference are required, fiber is preferred over electrical connections. This type of communication may transmit telemetry, audio, and video over long distances as well as smaller networks. Wavelength refers to the specific frequency of light used for transmitting data. Where optical fibres exhibit minimal attenuation (around 0.2 dB/km). This makes it ideal for long-distance communication as it minimizes signal loss. Bit rate is a channel that supports massive data transfer rates required for applications like streaming, cloud computing, and scientific research. Repeater spacing defines the maximum distance between optical amplifiers or repeaters in the fiber optic link. This channel allows light signals to travel long distances before requiring amplification or regeneration. This is achieved by using advanced technologies like Erbium-Doped Fibre Amplifiers (EDFAs) to compensate for signal attenuation over such distances PROPOSED METHOD A Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) system combined with Single Photon Avalanche Diode (SPAD) detectors is shown in Fig. 4 . A photon source at the sender's end initiates the process by emitting single photons, which are subsequently encoded using a polarizer to represent certain quantum states (e.g., utilizing polarization-based encoding like horizontal, vertical, or diagonal). These quantum states go toward the central relay via the quantum channel, which is a fiber optic link in this instance. There, a Bell-state measurement (BSM) is carried out using a SPAD detector and an additional polarizer. SPADs are perfect for detecting weak quantum signals and correcting for noise such as dark counts and after pulses because of their great sensitivity and temporal resolution. The results of the measurement are used to generate a random secret key, which is then shared securely between the sender and receiver over the fibre optic channel. The system is secure against detector-side-channel attacks due to the MDI-QKD design, which treats the detection system as untrusted. Step 1: Initialize the Quantum Key Distribution System Define the Si-APD with parameters are Efficiency, DCR & APP For Silicon Avalanche Photodiodes (Si APDs) in this paradigm, a fixed quantum efficiency of 0.7 is frequently employed since it represents a trade-off between high sensitivity and useful efficacy in optical communication and detection systems. For applications like QKD and PC, a DCR of 10 − 6 (1 count per second) is used because it represents a low noise level achievable with advanced single-photon detectors, including Si APDs. 10% of detection events are from AP rather than actual photons or dark counts, according to an APP of 0.1. This threshold is achievable with current detection technology and low enough to offer consistent performance in applications like QKD. Define the Fibre Optic Channel with parameters: Bit rate = 10 Tbps Repeater spacing = 1000 km Wavelength = 1.5 µm The repeater spacing of 1000 km allows light signals to travel long distances before requiring amplification or regeneration, and the wavelength of 1.5 µm (or 1550 nm) falls within the third optical transmission window, where optical fibers exhibit minimal attenuation (around 0.2 dB/km). This model's bit rate indicates that the channel can transmit 10 trillion bits of information per second, making it appropriate for contemporary high-speed communication systems. Step 2: Prepare Quantum States for the sender and Receiver Randomly assign quantum polarization states : Horizontal(H)→ |0⟩ Vertical(V) → |1⟩ Diagonal (+) → \(\:(\left|0\right.⟩+\left|1\right.⟩)/\surd\:2\) Anti-Diagonal (-) → \(\:(\left|0\right.⟩-\left|1\right.⟩)/\surd\:2\) Sender and receiver side polarization beam splitters, like rectilinear and diagonal, are used for measurement. Rectilinear polarizations are diagonal and anti-diagonal. Diagonal polarizations are horizontal and vertical. QBER=N error RESULTS & DISCUSSION The Qiskit Aer simulator was used to simulate 1000 photons to construct the suggested framework. The success of the system was assessed by computing and analyzing important performance characteristics, such as filtered key, final key length, quantum bit error rate (QBER), dark count rate, after-pulse probability, detector dead time, and total runtime. The Quantum Key Distribution (QKD) communication simulation results for qubit sizes ranging from 100 to 1000 are shown in Table 1 . In order to execute the protocol with a maximum capacity of 1000 qubits, the paper includes extensive metrics such as the shifting key length, final key length, dark count rate, after-pulse probability, detector dead time, and overall runtime. The parameters provide a comprehensive assessment of the system's functionality under practical circumstances. Table 1 Qubits parameters Qubits Shifted key Final Key QBER Dark count After pulse Dead time Runtime 100 53 35 0.3396 1 0 96 0.28 200 113 77 0.3018 4 1 206 2.26 300 144 99 0.3125 3 1 294 4.84 400 182 115 0.3681 4 1 397 9.89 500 260 167 0.3577 2 1 492 18.75 600 309 193 0.3754 8 5 582 30.72 700 346 206 0.4046 6 4 710 48.29 800 404 256 0.3663 12 3 806 74.81 900 437 284 0.3501 8 5 874 103.73 1000 492 316 0.3577 6 2 1020 138.02 Figure 5 : The application of 1000 qubits of transmitted data into the quantum channel and the reconciliation phase carried out through the classical channel are used to quantify the runtime execution in MDI-QKD. Quantum libraries created in MATLAB and Python were used to evaluate this QKD technique in a classical environment. The QBER found in these trials is high enough to make it easier to carry out QKD procedures and determine how long it takes to generate a secure key. Table 2 displays the simulation results following the addition of a SPAD to the detector end to improve single-photon detection. When SPAD is utilized, the QBER is decreased, the detector sensitivity increases, the dark count rate increases, the runtime varies according to the difficulty of managing noise, and the final key length is much enhanced. The limitations of employing real detector models in quantum key distribution methods are brought to light by these findings. Table 2 QBER with SPAD Qubits shifted Final Key QBER Dark count After pulse Dead time Time 100 53 52 0.0189 1 0 1 0.31 200 99 99 0 3 0 3 1.51 300 138 135 0.0217 8 0 8 4023 400 196 192 0.0204 8 0 8 10.24 500 228 225 0.0132 7 0 7 18.45 600 311 303 0.0257 12 0 12 31.29 700 346 340 0.0173 12 0 12 47.25 800 415 410 0.012 13 0 13 75.72 900 430 421 0.0209 17 0 17 107.63 1000 484 477 0.0145 17 0 17 136.59 Figure 6 : The diagram depicts the correlation between the QBER and the quantity of qubits communicated across a 1000 km Fibre-optic quantum channel, utilizing a SPAD for detection. As the total number of qubits rises, the QBER exhibits a decreasing pattern, signifying enhanced key precision and resistance. The results of incorporating physical detector deficiencies—dark counts, dead time, and after pulsing—into the QKD simulation are shown in Table 3 . Due to inaccurate detections and decreased photon detection accuracy, the QBER is significantly raised when these real noise components are included. Because more bits must be discarded during key sifting and error correction, the final key value decreases. The increased processing cost required to handle and lessen the influence of detector-induced noise in the simulation results in an increase in the overall runtime. Table 3 SPAD with Noise Qubits Shifted key Final Key QBER Dark count After pulse Dead time Jitter Thermal noise Runtime 100 53 52 0.0189 0 0 4 2 0 0.28 200 113 94 0.06 5 0 28 6 3 2.26 300 144 146 0.0267 5 0 14 0 2 4.84 400 182 184 0.0612 8 0 39 7 5 9.89 500 260 244 0.0469 7 0 44 13 2 18.75 600 309 299 0.0478 11 0 44 12 1 30.72 700 346 348 0.0413 7 0 68 19 8 48.29 800 404 390 0.0394 11 0 68 20 3 74.81 900 437 443 0.0453 15 0 102 17 19 103.73 1000 492 476 0.0556 21 0 112 22 13 138.02 Figure 7 : The graphic shows that when physical detector noise is added to the QKD system, the QBER increases dramatically. Flaws include dark counts, after-pulsing effects, and detector dead time, which lead to erroneous photon detections and spurious key bits and are primarily responsible for the increase in QBER. The security and effectiveness of key generation are impacted by the reduction in quantum signal detection quality brought on by several noise sources, which increases the frequency of bit mistakes. A comparison of the QBER in a QKD system under ideal (noise-free) and non-ideal (noisy) conditions is shown in Fig. 8 . The QBER remains relatively low in the absence of noise, indicating accurate detection and reliable key creation. However, due to inaccurate photon detection, physical detector flaws like dark counts, dead time, and after pulsing greatly raise the QBER. By increasing the system's ability to identify and evaluate different noise elements, the SPAD detector improves error estimates and enables more effective noise reduction strategies. The results of the simulation show how several physical and system-level factors affect QKD's effectiveness across a 1000 km fiber-optic link. Both the filtered and final key lengths improve as the number of qubits increases from 100 to 1000, and the QBER decreases, indicating higher key accuracy. When all detector flaws were eliminated, the QBER's range was consistently low, ranging from 0.3 to 0.4. With a maximum of 500 secure bits for 1000 qubits, the final key length showed a roughly linear scaling with the number of qubits. The noisy simulation, which included realistic detector imperfections such as a dark count rate of 5×10 − 6, an after-pulse probability of 1%, and a detector dead time of 10 µs, demonstrated a gradual increase in QBER. CONCLUSION This work thoroughly examines the effectiveness of QKD systems across long fiber-optic channels under both ideal and realistic physical conditions. The study highlights the significance of key elements, such as the number of qubits, detector noise (including dark counts, dead time, and after pulsing), and the application of SPADs to enhance single-photon detection. Under ideal circumstances, increasing the number of qubits reduces the QBER and increases key generation efficiency, according to simulation research. The practical difficulties encountered in real-world implementations are demonstrated by the fact that physical detector faults result in a decrease in the ultimate key length and a rise in QBER. The use of SPADs offers a significant advantage in noise detection and reduction, enabling improved security and dependability in critical generation. To match theoretical security with real-world implementation, this work emphasizes the need for accurate detector modeling and the necessity of using realistic noise generators in QKD simulations. The findings demonstrate the need for sophisticated noise reduction methods to improve the effectiveness and security of QKD systems, including single-photon selection, time-based gating, and superconducting nanowire single-photon detectors (SNSPDs). To increase the efficiency of quantum key distribution in practical applications, future research will concentrate on quantum error correction and adaptive noise suppression strategies. Declarations Competing Interests: The authors declare no competing interests. Funding Information: Not Applicable Author Contributions: J Suneetha: conceptualized the study, Methodology, Formal Analysis, conducted the experiments, and Drafting of the Manuscript. Smita Darandale: Supervision, Manuscript Review & Editing, and Final Approval. Data Availability Statement: Not Applicable Research Involving Human and/or Animals: Not Applicable Informed Consent: Not Applicable References Djordjevic, I.B.: Joint QKD-Post-Quantum Cryptosystems. IEEE Access. 8 , 154708–154712 (2020). https://doi.org/10.1109/access.2020.3018909 Biswas, C., Haque, M.M., Gupta, U.D.: A Modified Key Sifting Scheme With Artificial Neural Network-Based Key Reconciliation Analysis in Quantum Cryptography. 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Npj Quantum Inform. 4 (1) (2018). https://doi.org/10.1038/s41534-017-0057-8 Liu, B., Huang, R., Yang, Y., Xu, G.: Measurement-device-independent multi-party quantum key agreement. Front. Quantum Sci. Technol. (2023). 2 https://doi.org/10.3389/frqst.2023.1182637 Zapatero, V., Van Leent, T., Arnon-Friedman, R., Liu, W., Zhang, Q., Weinfurter, H., Curty, M.: Advances in device-independent quantum key distribution. Npj Quantum Inform. 9 (1) (2023). https://doi.org/10.1038/s41534-023-00684-x Pan, T., Zhou, R., Zhang, X.: Measurement-device-independent quantum secure direct communication based on quantum cover channel and multiple degrees of freedom of hyperentanglement. Phys. Scr. 100 (2), 025114 (2025). https://doi.org/10.1088/1402-4896/ada4f4 Lee, A., Castillo, A.T., Whitehill, C., Donaldson, R.: Quantum bit error rate, timing jitter dependency on multi-mode fibres. Opt. Express. 31 (4), 6076 (2023). https://doi.org/10.1364/oe.477156 Sharma, V.: Analysis of single photon detectors in differential phase shift quantum key distribution. Opt. Quant. Electron. 55 (10) (2023). https://doi.org/10.1007/s11082-023-05170-4 Cao, Y., Zhao, Y., Wang, Q., Zhang, J., Ng, S.X., Hanzo, L.: The evolution of Quantum Key Distribution Networks: On the road to the QInternet. IEEE Commun. Surv. Tutorials. 24 (2), 839–894 (2022). https://doi.org/10.1109/comst.2022.3144219 Hasan, K.F., Simpson, L., Baee, M.A.R., Islam, C., Rahman, Z., Armstrong, W., Gauravaram, P., McKague, M.: A Framework for Migrating to Post-Quantum Cryptography: Security Dependency Analysis and Case Studies. IEEE Access. 12 , 23427–23450 (2024). https://doi.org/10.1109/access.2024.3360412 Abushgra, A.: Variations of QKD protocols based on conventional system measurements: a literature review. Cryptography. 6 (1), 12 (2022). https://doi.org/10.3390/cryptography6010012 Shu, H.: Measurement-device-independent quantum key distribution protocols. Chin. J. Phys. 85 , 135–142 (2023b). https://doi.org/10.1016/j.cjph.2023.06.019 Rahmanpour, M., Erfanian, A., Afifi, A., Khaje, M., Fahimifar, M.H.: Implementable methods for characterizing single-photon avalanche diode parameters. Results Opt. 16 , 100709 (2024b). https://doi.org/10.1016/j.rio.2024.100709 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8711394","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":602857378,"identity":"05cfcacd-70d8-418a-90a6-4e8179eef05a","order_by":0,"name":"Suneetha J","email":"","orcid":"","institution":"GITAM University","correspondingAuthor":false,"prefix":"","firstName":"Suneetha","middleName":"","lastName":"J","suffix":""},{"id":602857379,"identity":"02adcf28-1732-46ef-ba86-2b08267a7c16","order_by":1,"name":"Smitha Darandale","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYFCCBBDBzMDPwNgAEThArBbJBsbGBtK0GByAWUNIi3x78rMPP3dYyxufX9z+4GcOgxzfjQT8WgzOPDOe2Xsm3XDbjYeNjb3bGIwlCWqRSDBm4G07zLjtxsHGBt5tDIkbCGmRn5H+mfFv22H7zTMONjb+3cZQT1ALw40cY2agLYkb+Bsbm4G2JBgQ9subYmbZtvTkGTcYG2fLbpMwnHnmAQGHtadvZnzbZm3b33/8wce322zk+Y4TchgcSIBVShCrHAT4D5CiehSMglEwCkYSAADba06W7ACW1wAAAABJRU5ErkJggg==","orcid":"","institution":"GITAM University","correspondingAuthor":true,"prefix":"","firstName":"Smitha","middleName":"","lastName":"Darandale","suffix":""}],"badges":[],"createdAt":"2026-01-27 14:09:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8711394/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8711394/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104499294,"identity":"283ee1e1-db72-4d2a-b3a9-3906b396e737","added_by":"auto","created_at":"2026-03-12 13:26:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":61256,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQKD process\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/da2e35dfbcf548fa64037a70.png"},{"id":104499263,"identity":"70748522-6d2b-422b-816f-fea1719580b9","added_by":"auto","created_at":"2026-03-12 13:26:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":128917,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSteps for QKD Protocol\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/6d6bd36a94ac80cb0beec18a.png"},{"id":104499322,"identity":"a00c21ab-3ea1-4cab-bf02-f71ccf3b3ce7","added_by":"auto","created_at":"2026-03-12 13:26:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":101710,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMDI-QKD protocol\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/60631be3c476892e5bcf94f1.png"},{"id":104499332,"identity":"d5910d5c-11c6-4207-9228-3fbe758e6b41","added_by":"auto","created_at":"2026-03-12 13:26:34","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":218686,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNoise detection model\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/e2dea6de56924813ec907adf.png"},{"id":104499349,"identity":"534c1571-6384-44eb-a9e9-310f0233f12b","added_by":"auto","created_at":"2026-03-12 13:26:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":75018,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQBER vs Qubits\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/c910c6367a6dbbd7f138a184.png"},{"id":104499289,"identity":"03f89268-f7d9-4bfb-825f-26959d3b539d","added_by":"auto","created_at":"2026-03-12 13:26:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":161999,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQBER vs Qubits (SPAD)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/21b0c07b733a67f073bf6329.png"},{"id":104499338,"identity":"2b209e75-0598-409e-9c75-95832564e647","added_by":"auto","created_at":"2026-03-12 13:26:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":174485,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQBER vs Qubits (Physical imperfections)\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/b64bf0db93700ecbfdb3308d.png"},{"id":104499376,"identity":"65409f23-c7de-43b2-bef0-2c043452aedf","added_by":"auto","created_at":"2026-03-12 13:26:47","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":135307,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison between Ideal \u0026amp; Noise\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/0ee09466b55ed249a3c26052.png"},{"id":106674057,"identity":"aa223f86-efe6-4b56-a0b2-c6124246372a","added_by":"auto","created_at":"2026-04-11 11:25:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2124166,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8711394/v1/6c91f175-2099-4c01-bd89-e894856948f1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spurious Pulse Detection in Fibre-Optic Channels Using Measurement-Device-Independent Quantum Key Distribution with Single-Photon Avalanche Photodiodes","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eIn view of the widespread usage of information systems in many facets of everyday life, there are many information security issues, and security threats are become more prevalent and intricate. Academics and business are becoming increasingly concerned about the security of personal data sent via the Internet. However, because of their greater processing capacity, the advent of quantum computers poses a serious threat to conventional cryptosystems. To create an encrypted connection between two users, a secret communication protocol employs a number of traditional public key cryptography [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e] primitives.\u003c/p\u003e \u003cp\u003eOne important area of quantum information science is quantum cryptography (QC) [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e], often known as quantum key distribution. Providing a totally secure data transfer between two parties—typically referred to as Alice (Sender) and Bob (Receiver)—is the main goal of quality control. While current encryption systems rely on mathematical laws, rendering transmitted messages potentially vulnerable to decoding, the underlying principles of quantum physics provide security and invulnerability to eavesdropping. According to the Shannon theory, if a transmission is encrypted using a random one-time key whose length corresponds to the message, it might not be decoded since only authorized users are aware of the key. The primary challenge in executing this strategy is the distribution of a secret quantum key among distant users.\u003c/p\u003e \u003cp\u003eThe photo photoelectric effect, in which photons transmit their energy to electrons in a substance and cause the electrons to be released, is the basis for how a single photon detector (SPD) operates. This phenomena is used by SPD to identify individual photons. The single-photon detector for incorrect pulses on the receiver's end is a problem in Quantum Key Distribution (QKD) [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e]. The method used to detect single photons is the single-photon avalanche diode in linear mode [\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA cutting-edge security method for sending safe keys is called Quantum Key Distribution (QKD). The foundation of this key distribution technique is quantum physics. Both the sender and the recipient of a secure message may identify efforts at eavesdropping thanks to QKD [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e]. In quantum physics, the discovery of eavesdropping within the quantum channel is guaranteed by Heisenberg's uncertainty principle. Furthermore, an eavesdropper cannot produce unexpected quantum states or replicate additional qubits. The two transmitting and receiving components of the QKD system are situated on opposing sides of the quantum channel. Highly sensitive data, including genetic, pharmacological, and personal medical records, is managed via a permanent secure storage network that uses QKD, secret sharing, and authentication methods. The increasing concern over data privacy suggests that this storage network may become a vital application of QKD.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e\u003c/p\u003e"},{"header":"LITERATURE SURVEY","content":"\u003cp\u003eIn their paper, Akram Youssry et al. [\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e] provide a novel technique for noise detection that combines quantum feature synthesis techniques with spectator qubits. The method consists of a two-phase protocol: an execution phase where real-time measurements of the spectator qubit offer information for the best control pulses sent to the data qubit, and a characterisation phase where a machine learning-based grey box model specifies noise profiles. This technique enhances qubit fidelity and aids in differentiating various noise patterns. However, this study's dependence on labeled characterisation data, which can be challenging to get in real-world circumstances, is a significant restriction. Furthermore, in dynamic quantum settings, the assumption that the noise influencing the spectator and data qubits is constant throughout time could not be true.\u003c/p\u003e\u003cp\u003eThe integrity of a two-state quantum bit commitment mechanism under realistic noise conditions is investigated by Ricardo Loura et al. [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. The authors use a combination of depolarizing channels, unitary development, and basis-dependent channels to describe errors caused by background noise and equipment defects, including sources, fibers, and detectors. The method makes use of information-theoretic criteria, such as fidelity and relative entropy, to evaluate the impact of noise and offer the best ways to cheat. The majority of the work is theoretical, and the proposed models might not accurately capture the complexities of practical implementations. Furthermore, although discussing noisy and confined quantum memory, the article's applicability to actual quantum communication systems is limited due to its lack of empirical support.\u003c/p\u003e\u003cp\u003eThe effectiveness of Single-Photon Avalanche Diodes (SPADs) in time-gated photon-counting applications is examined by Mahmoudi et al. [\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]. Delineating noise sources and failure mechanisms in SPAD detectors is likely the focus of the effort, which is crucial for applications that need precise photon detection. To evaluate SPAD performance under various conditions, experimental measurements are used to look at factors including jitter, after pulsing, and dark count rate. This research's dependence on specific SPAD designs, which could not be applicable to numerous models, is a major limitation. Furthermore, SPAD performance may be impacted by external factors like temperature fluctuations and electromagnetic interference, which may not be fully taken into account during the characterization process.\u003c/p\u003e\u003cp\u003eA technique for evaluating important SPAD characteristics, such as detection efficiency, dark count rate, timing jitter, and after-pulsing phenomena, was proposed by Rahmanpour et al. [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]. The procedure most likely involves controlled experimental setups where SPADs are exposed to certain light sources and their responses are measured using statistical analysis and time-correlated single-photon counting. The quality of the experimental equipment and the calibration of measuring devices have a major impact on the accuracy of these characterization techniques. Errors might be caused by external factors like temperature changes and ambient light, and the need for specialist equipment might make these processes inaccessible to all research institutes.\u003c/p\u003e\u003cp\u003eThe significance of security flaws in Quantum Key Distribution (QKD) systems caused by correlated intensity fluctuations in optical pulses is emphasized by Yoshino et al. [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e]. Presumably, the study offers a real-time pulse intensity monitoring and stabilization method or a protocol modification that reduces vulnerability to such fluctuations. The effectiveness of this countermeasure, which shows improvements in security and key generation rates under varied conditions, is evaluated by theoretical analysis and perhaps experimental validation. However, implementing such a countermeasure could be more difficult, requiring sophisticated hardware and signal processing techniques. Depending on the precise features of the intensity changes, trade-offs between increased security and system performance may occur, possibly leading to larger delays or lower key generation rates. Furthermore, although the countermeasure may mitigate one attack vector, additional potential vulnerabilities in QKD systems persist unexplored.\u003c/p\u003e\u003cp\u003eAccording to Liu et al. [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e], Quantum Key Agreement (QKA) has become a crucial cryptographic foundation, enabling secure multi-party key production that outperforms conventional methods. However, traditional QKA protocols have security vulnerabilities, particularly to detector-side-channel attacks that attackers might exploit. Measurement-Device-Independent (MDI) QKA methods have been put in place to reduce these risks by eliminating reliance on reliable measurement tools. By using post-selected Greenberger-Horne-Zeilinger (GHZ) states, the proposed MDI-QKA protocol enhances security by ensuring participant fairness and prevents any subset from independently determining the key. By assuming that just the state preparation devices are reliable, this method improves resilience against eavesdropping in comparison to previous MDI-QKA protocols.\u003c/p\u003e\u003cp\u003eNotwithstanding these gains, efficiency concerns remain, particularly with an increasing number of participants, demanding further study on optimizing critical production rates and mitigating noise-related issues for practical application.\u003c/p\u003e\u003cp\u003eThis paper includes\u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cp\u003eThis study presents an innovative modelling framework for MDI-QKD that integrates real-world defects of Single Photon Avalanche Diodes (SPAD), including dark count rate, after pulsing, and dead time.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIn contrast to idealized simulations, the simulation accurately reflects the influence of detector-level noise sources throughout a 1000 km fibre-optic link, offering a realistic performance assessment.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eA comparative study between optimal and noisy systems reveals the deterioration in QBER and key length, providing essential insights for the development of realistic quantum communication systems.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e"},{"header":"METHODOLOGIES","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Quantum key distribution\u003c/h2\u003e\n \u003cp\u003eDelivering individual photons, each encoded with a random quantum state, via fiber-optic channels between communication parties is how QKD [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e] works. As a series of qubits, these quantum states represent binary values and serve as the quantum equivalent of classical bits. Each photon interacts with a beam splitter upon arrival, which randomly directs it to one of two receptors. Using a classical channel, the receiver records the measurement data and communicates to the sender the fundamental decisions made for measurement. In order to identify similar events, the sender then compares these with the original preparation foundation. Measurements that are inconsistent or unclear are removed; only photon measurements when the preparation and measuring bases match are kept. The resultant shared bit sequence, referred to as the sifting key, can then be utilized for safe data encryption.\u003c/p\u003e\n \u003cp\u003eQKD protocols are performed in five stages [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/p\u003e\n \u003cp\u003e1.\u0026nbsp; \u0026nbsp;Qubit preparation transmission\u003c/p\u003e\n \u003cp\u003e\u0026middot; At this stage, the sender prepares quantum states (qubits) on a selected basis, such as the rectilinear (∣0\u0026rang;,\u0026nbsp;∣1\u0026rang;) or diagonal (∣+\u0026rang;,\u0026nbsp;∣\u0026minus;\u0026rang;) basis.\u003c/p\u003e\n \u003cp\u003e\u0026middot; The quantum bits are then sent to the recipient via a quantum channel, usually via a fibre optic or free-space connection.\u003c/p\u003e\n \u003cp\u003e\u0026middot; During transmission, quantum states may be influenced by noise and any eavesdropping efforts.\u003c/p\u003e\n \u003cp\u003e2.\u0026nbsp; \u0026nbsp;Shifting\u003c/p\u003e\n \u003cp\u003e\u0026middot; The receiver randomly assesses the received qubits utilizing one of the two available bases.\u003c/p\u003e\n \u003cp\u003e\u0026middot; After measurement, Sender and Receiver engage in classical communication to compare the bases utilized for each qubit, without disclosing the actual bit values.\u003c/p\u003e\n \u003cp\u003e\u0026middot; They save just the measurements where each utilized the identical foundation, so creating a mutual filtered key.\u003c/p\u003e\n \u003cp\u003e3.\u0026nbsp; \u0026nbsp;Parameter estimation\u003c/p\u003e\n \u003cp\u003e\u0026middot; Sender and Receiver publicly compare a portion of their filtered key to identify the existence of an eavesdropper (Eve).\u003c/p\u003e\n \u003cp\u003e\u0026middot; They compute the QBER, which quantifies differences among their key bits.\u003c/p\u003e\n \u003cp\u003e\u0026middot; Should the mistake rate be above a certain threshold, they infer the existence of eavesdropping and invalidate the key. Alternatively, they advance to the subsequent stage.\u003c/p\u003e\n \u003cp\u003e4.\u0026nbsp; \u0026nbsp;Post processing\u003c/p\u003e\n \u003cp\u003e\u0026middot; Correction of mistakes: Due to the possibility of introduction of mistakes by noise or mild disruptions, both Sender and Receiver employ conventional error correction methods [6] (e.g., Cascade, Winnow) to resolve disparities.\u003c/p\u003e\n \u003cp\u003e\u0026middot; Privacy Amplification: To eliminate whatever incomplete information that an eavesdropper may have acquired, Sender and Receiver utilize hash algorithms or compression methods to produce a concise, highly secure final key.\u003c/p\u003e\n \u003cp\u003e5. \u0026nbsp; Authentication\u003c/p\u003e\n\u003c/div\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eSender and Receiver employ traditional cryptographic authentication [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], such as Message Authentication Codes, to safeguard against man-in-the-middle attacks and ensure the integrity of their communications.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eUpon authentication, the definitive secret key is prepared for the safe encryption of communications.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e provides about detailed explanation steps how the key between the sender and receiver.\u003c/p\u003e \u003cp\u003eQKD is a fundamental basis in QC. In a QKD protocol, many untrusted parties can collaboratively establish a shared key, ensuring that each party has equal influence on the key and that no subset can independently determine it. Nonetheless, in real QKD, the flaws in the detectors of the participants can be used to undermine the security and integrity of QKD. A MDI- QKD protocol is suggested to eliminate all detector-side-channel vulnerabilities.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Measurement device independent protocol (MDI)\u003c/h2\u003e \u003cp\u003eMDI-QKD is a quantum cryptography technology created to mitigate and eradicate security risks stemming from flawed or untrusted measurement equipment.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMDI-QKD procedure\u003c/p\u003e \u003cp\u003e1. Qubit Preparation:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA and B independently generate weak coherent pulses (WCPs) utilizing randomly selected basis states (ZZ or XX) and intensity configurations.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe probability for base selection is\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003ePZ Z-basis \u003cb\u003e(1)\u003c/b\u003e\u003c/p\u003e \u003cp\u003ePX\u0026thinsp;=\u0026thinsp;1 \u0026ndash; PZ X-basis. \u003cb\u003e(2)\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIntensity settings (γs, γv, γw) are selected with probabilities ps, pv, pw, respectively. The intensities are refined for key generation and parameter estimation.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e2. Qubit Encoding\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA and B encode random data into their generated WCPs utilizing an encoding strategy, such as polarization or phase encoding [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe encoded pulses are transmitted to an untrusted relay (e.g., Charlie C) using quantum channels.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e3. Bell state Measurement (BSM) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe untrusted relay executes a BSM on the incoming pulses from A and B.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSuccessful BSM outcomes demonstrate entanglement-like correlations between A's and B's states, utilized for key generation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eC openly discloses the measurement findings while withholding any details on the encoded bits.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e4. Qubit shifting\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA and B evaluate their base selections over a classical channel. Only data utilizing the identical base is preserved for subsequent processing.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThis stage eliminates incongruent basis data to maintain consistency in key generation.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e5. Parameter Estimation\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAlice and Bob examine a portion of their retained data to assess mistake rates and identify possible eavesdropping.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDecoy-state approaches are employed to precisely estimate the contribution of single-photon pulses, hence safeguarding against photon-number-splitting attackers.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e6. Reconciliation\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA and B utilize conventional error correction techniques to align their raw keys into congruent shared keys.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDiscrepancies arising from noise or channel defects are rectified at this phase.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e7. Privacy Amplification\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA and B [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] employ privacy amplification techniques to remove whatever incomplete knowledge that an eavesdropper may have acquired.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThis condenses the raw key into a more concise yet entirely secure final key.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Dark count rate\u003c/h2\u003e \u003cp\u003eThe DCR [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] can be described as the number of pulses per second recorded in the absence of light, specifically measured without the presence of photons [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The inaccurate detection events mostly stem from heat sources and may thus be significantly mitigated by employing a cooled detector type.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:DCR=\\frac{\\text{N}\\text{D}}{\\text{D}\\text{u}\\text{r}\\text{a}\\text{t}\\text{i}\\text{o}\\text{n}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eND is the summation of dark counts detected over a period of duration\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDuration is the measurement of time in seconds\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.4 After pulse rate\u003c/h2\u003e \u003cp\u003eThe After Pulse Rate (APR) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] is the proportion of observed events in a photon detector that lead to incorrect secondary detections caused by charge trapping and release delays [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. It measures the likelihood that a dark count or a legitimate photon detection induces an extra false count.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:APR=\\frac{\\text{N}\\text{A}}{\\sum\\:NT}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eNA is the number of after-pulse events detected\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eNT is the total number of detected counts (including dark counts, after pulse, and single photons)\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e\u003cb\u003e3.5 Quantum bit error rate\u003c/b\u003e [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/h2\u003e \u003cp\u003eThe QBER quantifies faults in a QKD system. It denotes the proportion of erroneous bits to the overall quantity of sent bits in the filtered key.\u003c/p\u003e \u003cp\u003eQBER=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{NE}{\\sum\\:NS}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003e(5)\u003c/b\u003e\u003c/p\u003e \u003cp\u003eWhere\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eNE=number of erroneous bits in the shifted key\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eNS=Total number of shifted key bits\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.6 SPAD\u003c/h2\u003e \u003cp\u003eIn addition to their single-photon sensitivity, high detection efficiency, low dark count rates, and low timing jitter, Single Photon Avalanche Diodes (SPADs), particularly InGaAs/InP planar-geometry devices designed for the 1.55 \u0026micro;m telecommunications wavelength, are incredibly promising detectors for QKD [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. To meet the strict requirements of QKD systems, the SPADs go through extensive modeling, manufacturing, and characterization. This allows for safe key distribution across long distances at reasonable key rates. Recent advances include GHz-gated InGaAs/InP single-photon avalanche diodes (SPADs) that are electrically cooled and achieve detection efficiency close to 6% and dark count probabilities as low as 2.8\u0026times;10⁻\u0026sup2;. These developments have made it possible for fiber optics to achieve secure key speeds of 24 kbit/s across a 100-kilometer distance.\u003c/p\u003e \u003cp\u003eThe probability that an incoming photon is successfully detected photon detection probability\u003c/p\u003e \u003cp\u003ePDP\u0026thinsp;=\u0026thinsp;QE*PP \u003cb\u003e(6)\u003c/b\u003e\u003c/p\u003e \u003cp\u003eWhere QE=Quantum Efficiency\u003c/p\u003e \u003cp\u003ePP=Photon probability\u003c/p\u003e \u003cp\u003eDark counts are false detections due to thermal or electronic noise: Dark count probability (DCP)\u003c/p\u003e \u003cp\u003eDCP=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:1-{e}^{-DCR.T\\:window}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003e(7)\u003c/b\u003e\u003c/p\u003e \u003cp\u003eWhere DCR=Dark count Rate, counts per second\u003c/p\u003e \u003cp\u003eTwindow =detection time window\u003c/p\u003e \u003cp\u003eAfter pulse probability (APP) after pulsing occurs when a previously detected photon triggers a secondary false detection. The probability of APP\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eAPP\u0026thinsp;=\u0026thinsp;Ap*P \u003cb\u003e(8)\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere AP Probability of an after pulse per detection\u003c/p\u003e \u003cp\u003eP=photon detected\u003c/p\u003e \u003cp\u003eTotal count probability TCP\u0026thinsp;=\u0026thinsp;PDP+DCP\u0026thinsp;+\u0026thinsp;APP (9)\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Fibre optic channel\u003c/h2\u003e \u003cp\u003eFiber optic communication is an optical communication method that uses visible or infrared light pulses to send data across an optical fiber. Light functions as an electromagnetic wave that has been altered to convey data [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. When high bandwidth, long distances, or resistance to electromagnetic interference are required, fiber is preferred over electrical connections. This type of communication may transmit telemetry, audio, and video over long distances as well as smaller networks.\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eWavelength refers to the specific frequency of light used for transmitting data. Where optical fibres exhibit minimal attenuation (around 0.2 dB/km). This makes it ideal for long-distance communication as it minimizes signal loss.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eBit rate is a channel that supports massive data transfer rates required for applications like streaming, cloud computing, and scientific research.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRepeater spacing defines the maximum distance between optical amplifiers or repeaters in the fiber optic link. This channel allows light signals to travel long distances before requiring amplification or regeneration. This is achieved by using advanced technologies like Erbium-Doped Fibre Amplifiers (EDFAs) to compensate for signal attenuation over such distances\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003ePROPOSED METHOD\u003c/h3\u003e\n\u003cp\u003eA Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) system combined with Single Photon Avalanche Diode (SPAD) detectors is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. A photon source at the sender's end initiates the process by emitting single photons, which are subsequently encoded using a polarizer to represent certain quantum states (e.g., utilizing polarization-based encoding like horizontal, vertical, or diagonal). These quantum states go toward the central relay via the quantum channel, which is a fiber optic link in this instance. There, a Bell-state measurement (BSM) is carried out using a SPAD detector and an additional polarizer. SPADs are perfect for detecting weak quantum signals and correcting for noise such as dark counts and after pulses because of their great sensitivity and temporal resolution. The results of the measurement are used to generate a random secret key, which is then shared securely between the sender and receiver over the fibre optic channel. The system is secure against detector-side-channel attacks due to the MDI-QKD design, which treats the detection system as untrusted.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 1: Initialize the Quantum Key Distribution System\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eDefine the Si-APD with parameters are Efficiency, DCR \u0026amp; APP\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFor Silicon Avalanche Photodiodes (Si APDs) in this paradigm, a fixed quantum efficiency of 0.7 is frequently employed since it represents a trade-off between high sensitivity and useful efficacy in optical communication and detection systems. For applications like QKD and PC, a DCR of 10\u0026thinsp;\u0026minus;\u0026thinsp;6 (1 count per second) is used because it represents a low noise level achievable with advanced single-photon detectors, including Si APDs. 10% of detection events are from AP rather than actual photons or dark counts, according to an APP of 0.1. This threshold is achievable with current detection technology and low enough to offer consistent performance in applications like QKD.\u003c/p\u003e \u003cp\u003eDefine the \u003cb\u003eFibre Optic Channel\u003c/b\u003e with parameters:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eBit rate\u0026thinsp;=\u0026thinsp;10 Tbps\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRepeater spacing\u0026thinsp;=\u0026thinsp;1000 km\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eWavelength\u0026thinsp;=\u0026thinsp;1.5 \u0026micro;m\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe repeater spacing of 1000 km allows light signals to travel long distances before requiring amplification or regeneration, and the wavelength of 1.5 \u0026micro;m (or 1550 nm) falls within the third optical transmission window, where optical fibers exhibit minimal attenuation (around 0.2 dB/km). This model's bit rate indicates that the channel can transmit 10 trillion bits of information per second, making it appropriate for contemporary high-speed communication systems.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 2: Prepare Quantum States for the sender and Receiver\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eRandomly assign quantum polarization states\u003c/b\u003e:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eHorizontal(H)\u0026rarr; |0⟩\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eVertical(V) \u0026rarr; |1⟩\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDiagonal \u003cb\u003e(+)\u003c/b\u003e \u0026rarr;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(\\left|0\\right.⟩+\\left|1\\right.⟩)/\\surd\\:2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAnti-Diagonal \u003cb\u003e(-)\u003c/b\u003e \u0026rarr; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(\\left|0\\right.⟩-\\left|1\\right.⟩)/\\surd\\:2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eSender and receiver side polarization beam splitters, like rectilinear and diagonal, are used for measurement. Rectilinear polarizations are diagonal and anti-diagonal. Diagonal polarizations are horizontal and vertical. QBER=N\u003csub\u003eerror\u003c/sub\u003e\u003c/p\u003e"},{"header":"RESULTS \u0026 DISCUSSION","content":"\u003cp\u003eThe Qiskit Aer simulator was used to simulate 1000 photons to construct the suggested framework. The success of the system was assessed by computing and analyzing important performance characteristics, such as filtered key, final key length, quantum bit error rate (QBER), dark count rate, after-pulse probability, detector dead time, and total runtime.\u003c/p\u003e \u003cp\u003eThe Quantum Key Distribution (QKD) communication simulation results for qubit sizes ranging from 100 to 1000 are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In order to execute the protocol with a maximum capacity of 1000 qubits, the paper includes extensive metrics such as the shifting key length, final key length, dark count rate, after-pulse probability, detector dead time, and overall runtime. The parameters provide a comprehensive assessment of the system's functionality under practical circumstances.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQubits parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQubits\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShifted key\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFinal Key\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eQBER\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDark count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAfter pulse\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDead time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRuntime\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e2.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e294\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e4.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3681\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e397\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e9.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3577\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e18.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3754\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e582\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e30.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e710\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e48.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e74.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e103.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3577\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e138.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e: The application of 1000 qubits of transmitted data into the quantum channel and the reconciliation phase carried out through the classical channel are used to quantify the runtime execution in MDI-QKD. Quantum libraries created in MATLAB and Python were used to evaluate this QKD technique in a classical environment. The QBER found in these trials is high enough to make it easier to carry out QKD procedures and determine how long it takes to generate a secure key.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displays the simulation results following the addition of a SPAD to the detector end to improve single-photon detection. When SPAD is utilized, the QBER is decreased, the detector sensitivity increases, the dark count rate increases, the runtime varies according to the difficulty of managing noise, and the final key length is much enhanced. The limitations of employing real detector models in quantum key distribution methods are brought to light by these findings.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQBER with SPAD\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQubits\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eshifted\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFinal Key\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eQBER\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDark count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAfter pulse\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDead time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0189\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e138\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e18.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0257\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e31.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e47.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e415\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e75.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e107.63\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e484\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e136.59\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e: The diagram depicts the correlation between the QBER and the quantity of qubits communicated across a 1000 km Fibre-optic quantum channel, utilizing a SPAD for detection. As the total number of qubits rises, the QBER exhibits a decreasing pattern, signifying enhanced key precision and resistance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results of incorporating physical detector deficiencies\u0026mdash;dark counts, dead time, and after pulsing\u0026mdash;into the QKD simulation are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Due to inaccurate detections and decreased photon detection accuracy, the QBER is significantly raised when these real noise components are included. Because more bits must be discarded during key sifting and error correction, the final key value decreases. The increased processing cost required to handle and lessen the influence of detector-induced noise in the simulation results in an increase in the overall runtime.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSPAD with Noise\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eQubits\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShifted key\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFinal Key\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eQBER\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDark count\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAfter pulse\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDead time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eJitter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eThermal noise\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eRuntime\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0189\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e2.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e4.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e184\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e9.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0469\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e18.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0478\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e30.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0413\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e48.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e74.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e443\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0453\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e103.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e138.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e: The graphic shows that when physical detector noise is added to the QKD system, the QBER increases dramatically. Flaws include dark counts, after-pulsing effects, and detector dead time, which lead to erroneous photon detections and spurious key bits and are primarily responsible for the increase in QBER. The security and effectiveness of key generation are impacted by the reduction in quantum signal detection quality brought on by several noise sources, which increases the frequency of bit mistakes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA comparison of the QBER in a QKD system under ideal (noise-free) and non-ideal (noisy) conditions is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The QBER remains relatively low in the absence of noise, indicating accurate detection and reliable key creation. However, due to inaccurate photon detection, physical detector flaws like dark counts, dead time, and after pulsing greatly raise the QBER. By increasing the system's ability to identify and evaluate different noise elements, the SPAD detector improves error estimates and enables more effective noise reduction strategies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results of the simulation show how several physical and system-level factors affect QKD's effectiveness across a 1000 km fiber-optic link. Both the filtered and final key lengths improve as the number of qubits increases from 100 to 1000, and the QBER decreases, indicating higher key accuracy. When all detector flaws were eliminated, the QBER's range was consistently low, ranging from 0.3 to 0.4. With a maximum of 500 secure bits for 1000 qubits, the final key length showed a roughly linear scaling with the number of qubits. The noisy simulation, which included realistic detector imperfections such as a dark count rate of 5\u0026times;10\u0026thinsp;\u0026minus;\u0026thinsp;6, an after-pulse probability of 1%, and a detector dead time of 10 \u0026micro;s, demonstrated a gradual increase in QBER.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eThis work thoroughly examines the effectiveness of QKD systems across long fiber-optic channels under both ideal and realistic physical conditions. The study highlights the significance of key elements, such as the number of qubits, detector noise (including dark counts, dead time, and after pulsing), and the application of SPADs to enhance single-photon detection. Under ideal circumstances, increasing the number of qubits reduces the QBER and increases key generation efficiency, according to simulation research. The practical difficulties encountered in real-world implementations are demonstrated by the fact that physical detector faults result in a decrease in the ultimate key length and a rise in QBER. The use of SPADs offers a significant advantage in noise detection and reduction, enabling improved security and dependability in critical generation. To match theoretical security with real-world implementation, this work emphasizes the need for accurate detector modeling and the necessity of using realistic noise generators in QKD simulations. The findings demonstrate the need for sophisticated noise reduction methods to improve the effectiveness and security of QKD systems, including single-photon selection, time-based gating, and superconducting nanowire single-photon detectors (SNSPDs). To increase the efficiency of quantum key distribution in practical applications, future research will concentrate on quantum error correction and adaptive noise suppression strategies.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompeting Interests:\u0026nbsp;\u003c/strong\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Information:\u003c/strong\u003e Not Applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e \u003cstrong\u003eJ Suneetha:\u003c/strong\u003e conceptualized the study, Methodology, Formal Analysis, conducted the experiments, and Drafting of the Manuscript. \u003cstrong\u003eSmita Darandale:\u003c/strong\u003e Supervision, Manuscript Review \u0026amp;amp; Editing, and Final Approval.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement:\u0026nbsp;\u003c/strong\u003eNot Applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResearch Involving Human and/or Animals:\u0026nbsp;\u003c/strong\u003eNot Applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInformed Consent:\u0026nbsp;\u003c/strong\u003eNot Applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDjordjevic, I.B.: Joint QKD-Post-Quantum Cryptosystems. 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Results Opt. \u003cb\u003e16\u003c/b\u003e, 100709 (2024b). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.rio.2024.100709\u003c/span\u003e\u003cspan address=\"10.1016/j.rio.2024.100709\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Measure Device Independent Quantum key distribution protocol (MDI-QKD), Single Photon Avalanche diode (SPAD), Dark count Rate (DCR), After pulse Rate (APR), Quantum bit error rate (QBER)","lastPublishedDoi":"10.21203/rs.3.rs-8711394/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8711394/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe safe exchange of cryptographic keys is made possible by Quantum Key Distribution (QKD), which makes use of the basic ideas of quantum physics. Quantum Bit Error Rate (QBER), key generation rate, and transmission distance are important performance measures in QKD systems. Nevertheless, undesired noise sources that impair system performance, such dark counts and afterpulses, restrict traditional QKD implementations. The Measurement-Device-Independent QKD (MDI-QKD) protocol and Single Photon Avalanche Diodes (SPADs) for single-photon detection are combined in this research to create an improved QKD model. All detector-side-channel weaknesses are naturally eliminated by the MDI-QKD protocol, while SPADs' excellent sensitivity and temporal precision allow for precise noise source detection and characterisation, including dark count and afterpulse rates. When compared to conventional QKD systems, the suggested method performs better when assessed using QBER. According to experimental findings, including SPADs into the MDI-QKD architecture greatly improves the security and effectiveness of quantum communication systems by detecting detector-induced errors.\u003c/p\u003e","manuscriptTitle":"Spurious Pulse Detection in Fibre-Optic Channels Using Measurement-Device-Independent Quantum Key Distribution with Single-Photon Avalanche Photodiodes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-12 13:24:39","doi":"10.21203/rs.3.rs-8711394/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"51e97fa4-62c2-495b-8b79-1a1d345e0928","owner":[],"postedDate":"March 12th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-11T11:24:31+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-12 13:24:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8711394","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8711394","identity":"rs-8711394","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}