Economic Decoupling Probability: A Quantum Analogy of Characterizing Bell State Errors and Noise on Real IBM Quantum Hardware

Accurate generation and measurement of entangled states, such as the Bell state |Φ⁺⟩, are crucial benchmarks for assessing the capabilities and variability of Noisy Intermediate-Scale Quantum (NISQ) hardware. This work benchmarks the fidelity of preparing the |Φ⁺⟩ = (|00⟩ + |11⟩)/√2 state on different qubit pairs ([2, 3] and [7, 8]) of the ibm_kyiv quantum processor over multiple runs (N=5) and employs the deviation from perfect correlation as a quantitative analogy for the probability of unexpected decoupling in systems expected to exhibit strong correlation, such as linked economic indicators. Implementing the standard Hadamard and CNOT gate sequence for 4096 shots per run using the qiskit-ibm-runtime SamplerV2 primitive, we characterized the state preparation and measurement fidelity and applied mthree-based readout error mitigation. Experimental raw results revealed significant variability between layouts, yielding mean anti-correlated outcome probabilities P(Anti) = P(01) + P(10) of approximately 1.6% (±0.3%) for layout [2, 3] and 9.2% (±0.8%) for layout [7, 8]. This performance difference strongly correlated with reported hardware calibration metrics, particularly average readout error rates. Readout error mitigation successfully reduced P(Anti) to near-zero values (≤0.1%) for both layouts, achieving corrected correlated outcome probabilities P(Corr) = P(00) + P(11) of ~99.9-100.0%. Within our conceptual framework, the range of raw P(Anti) serves as a quantitative analogue for the likelihood of 'unexpected decoupling' under different inherent noise conditions, while the mitigated results suggest the potential to isolate underlying system dynamics from measurement noise. This research provides concrete multi-run fidelity benchmarks for ibm_kyiv, demonstrates the effectiveness of error mitigation, highlights performance variability linked to calibration data, and quantifies a range for the proposed economic uncertainty analogy.