Machine Learning-Enhanced Entanglement Characterization in Bi-partite Ququart Systems

Machine Learning-Enhanced Entanglement Characterization in Bi-partite Ququart Systems | 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 Machine Learning-Enhanced Entanglement Characterization in Bi-partite Ququart Systems S. K. Rithvik Sreekantham, R. P. Singh Singh, Shashi Prabhakar Prabhakar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6486345/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract We present a systematic comparative analysis of machine learning and traditional approaches for quantum entanglement characterization in bi-partite ququart systems. Quantifying entanglement traditionally requires full quantum state tomography, necessitating $N_{mub}^2D^2N_{cop}$ measurements, where $N_{mub}$ is the number of mutually unbiased bases, $D$ is the subsystem dimensionality, and $N_{cop}$ is the number of identical copies. For ququart systems with $D=4$, this translates to hundreds of distinct measurement settings, each requiring multiple copies ($N_{cop}$ typically in thousands)—resulting in hundreds of thousands of total measurements in practice. Our research demonstrates that neural networks achieve comparable or superior accuracy with orders of magnitude fewer measurement settings. We evaluate three architectures—Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Transformer—against Maximum Likelihood Estimation (MLE) and Bayesian methods across measurement counts ranging from 10 to 400. Neural approaches achieve up to 1650× faster computation times compared to traditional methods while maintaining competitive accuracy. At 100 measurements, the Transformer achieves Mean Squared Error (MSE) of $1.49 \times 10^{-1}$, while MLE yields $2.04 \times 10^{-1}$—over 10× higher error—despite taking 178 times longer. All neural methods in our study show error reduction scaling as approximately $1/\sqrt{N}$ with increased measurements. While this observed scaling might be influenced by our specific architectures, it provides important practical guidance for experimental design. The Transformer architecture demonstrates exceptional sample efficiency, achieving with 100 measurements what traditional methods require 250-400 measurements to accomplish—a significant advantage for resource-constrained quantum experiments. This research provides a viable pathway for real-time entanglement characterization in higher-dimensional quantum systems where traditional methods become computationally prohibitive. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 11 Nov, 2025 Reviewers agreed at journal 14 Jul, 2025 Reviews received at journal 02 Jul, 2025 Reviewers agreed at journal 09 Jun, 2025 Reviewers invited by journal 08 Jun, 2025 Editor assigned by journal 01 Jun, 2025 Submission checks completed at journal 20 Apr, 2025 First submitted to journal 19 Apr, 2025 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6486345","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":468588900,"identity":"b41e18ed-129d-4947-841b-d1398485e40c","order_by":0,"name":"S. K. 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