{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:15:06Z","timestamp":1760058906198,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T00:00:00Z","timestamp":1747008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Oak Ridge National Laboratory (ORNL)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Hybrid quantum\u2013classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum\u2013classical interface (QCI)\u2014the boundary enabling these systems\u2014introduces unique and largely unexplored security vulnerabilities. This position paper proposes using entropy-based metrics to monitor and enhance security, specifically at the QCI. We present a theoretical security outline that leverages well-established information-theoretic entropy measures, such as Shannon entropy, von Neumann entropy, and quantum relative entropy, to detect anomalous behaviors and potential breaches at the QCI. By linking entropy fluctuations to scenarios of practical relevance\u2014including quantum key distribution, quantum sensing, and hybrid control systems\u2014we promote the potential value and applicability of entropy-based security monitoring. While explicitly acknowledging practical limitations and theoretical assumptions, we argue that entropy-based metrics provide a complementary approach to existing security methods, inviting further empirical studies and theoretical refinements that can strengthen future quantum technologies.<\/jats:p>","DOI":"10.3390\/e27050517","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T12:18:06Z","timestamp":1747052286000},"page":"517","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy of the Quantum\u2013Classical Interface: A Potential Metric for Security"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3130-1247","authenticated-orcid":false,"given":"Sarah","family":"Chehade","sequence":"first","affiliation":[{"name":"Quantum Information Science Section, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"},{"name":"Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2324-2489","authenticated-orcid":false,"given":"Joel A.","family":"Dawson","sequence":"additional","affiliation":[{"name":"Resilient Cyber-Physical Systems Section, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"},{"name":"Cyber Resilience and Intelligence Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2104-5641","authenticated-orcid":false,"given":"Stacy","family":"Prowell","sequence":"additional","affiliation":[{"name":"Resilient Cyber-Physical Systems Section, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"},{"name":"Cyber Resilience and Intelligence Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4736-4157","authenticated-orcid":false,"given":"Ali","family":"Passian","sequence":"additional","affiliation":[{"name":"Quantum Information Science Section, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"},{"name":"Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"032209","DOI":"10.1103\/PhysRevA.109.032209","article-title":"Hybrid classical-quantum systems in terms of moments","volume":"109","author":"Brizuela","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"042626","DOI":"10.1103\/PhysRevA.111.042626","article-title":"Simulating quantum-classical interfaces via the Lindblad master equation","volume":"111","author":"Passian","year":"2025","journal-title":"Phys. Rev. A"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wiseman, H.M., and Milburn, G.J. (2009). Quantum Measurement and Control, Cambridge University Press.","DOI":"10.1017\/CBO9780511813948"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cong, S. (2014). Control of Quantum Systems: Theory and Methods, John Wiley & Sons.","DOI":"10.1002\/9781118608135"},{"key":"ref_5","first-page":"012007","article-title":"Quantum-classical hybrid dynamics\u2014A summary","volume":"Volume 442","author":"Elze","year":"2013","journal-title":"Proceedings of the Journal of Physics: Conference Series"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.22331\/q-2023-07-26-1068","article-title":"Quantum-Classical Hybrid Systems and their Quasifree Transformations","volume":"7","author":"Dammeier","year":"2023","journal-title":"Quantum"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1073\/pnas.17.5.315","article-title":"Dynamical systems of continuous spectra","volume":"17","author":"Koopman","year":"1931","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"22A552","DOI":"10.1063\/1.4767931","article-title":"Quantum-classical path integral: I. Classical memory and weak quantum nonlocality","volume":"137","author":"Lambert","year":"2012","journal-title":"J. Chem. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1146\/annurev-physchem-082620-021809","article-title":"Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics","volume":"73","author":"Ananth","year":"2022","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1063\/1.459170","article-title":"Molecular dynamics with electronic transitions","volume":"93","author":"Tully","year":"1990","journal-title":"J. Chem. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"22A301","DOI":"10.1063\/1.4757762","article-title":"Perspective: Nonadiabatic dynamics theory","volume":"137","author":"Tully","year":"2012","journal-title":"J. Chem. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1103\/PhysRevA.56.162","article-title":"Mixing quantum and classical mechanics","volume":"56","author":"Prezhdo","year":"1997","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8919","DOI":"10.1063\/1.478811","article-title":"Mixed quantum-classical dynamics","volume":"110","author":"Kapral","year":"1999","journal-title":"J. Chem. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1146\/annurev.physchem.57.032905.104702","article-title":"Progress in the theory of mixed quantum-classical dynamics","volume":"57","author":"Kapral","year":"2006","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"014005","DOI":"10.1088\/0031-8949\/2014\/T163\/014005","article-title":"Entanglement dynamics in a quantum\u2014Classical hybrid of two q-bits and one oscillator","volume":"T163","author":"Fratino","year":"2014","journal-title":"Phys. Scr."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sergi, A., Lamberto, D., Migliore, A., and Messina, A. (2023). Quantum\u2013Classical Hybrid Systems and Ehrenfest\u2019s Theorem. Entropy, 25.","DOI":"10.3390\/e25040602"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7026","DOI":"10.1021\/acs.chemrev.7b00577","article-title":"Recent Advances and Perspectives on Nonadiabatic Mixed Quantum\u2013Classical Dynamics","volume":"118","author":"Barbatti","year":"2018","journal-title":"Chem. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Goldsmith, A. (2005). Wireless Communications, Cambridge University Press.","DOI":"10.1017\/CBO9780511841224"},{"key":"ref_19","unstructured":"Stallings, W. (2016). Cryptopgraphy and Network Security: Principles and Practice, Pearson. [4th ed.]. Available online: https:\/\/www.pearson.com\/en-us\/subject-catalog\/p\/cryptography-and-network-security-principles-and-practice\/P200000003477\/9780135764213."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Momot, F., Bratus, S., Hallberg, S.M., and Patterson, M.L. (2016, January 3\u20134). The Seven Turrets of Babel: A Taxonomy of LangSec Errors and How to Expunge Them. Proceedings of the 2016 IEEE Cybersecurity Development (SecDev), Boston, MA, USA.","DOI":"10.1109\/SecDev.2016.019"},{"key":"ref_21","unstructured":"Anderson, R.J. (2010). Security Engineering: A Guide to Building Dependable Distributed Systems, John Wiley & Sons."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4469","DOI":"10.1098\/rsta.2011.0487","article-title":"Decoherence and the conditions for the classical control of quantum systems","volume":"370","author":"Milburn","year":"2012","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Coffey, W.T., Kalmykov, Y.P., and Waldron, J.T. (2004). The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering, World Scientific.","DOI":"10.1142\/9789812795090"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"023106","DOI":"10.1088\/1742-5468\/ab6de2","article-title":"Quantum Langevin equation","volume":"2020","year":"2020","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_25","unstructured":"Gardiner, C., and Zoller, P. (2004). Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, Springer Science & Business Media. Available online: https:\/\/link.springer.com\/book\/9783540223016."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Walls, D., and Milburn, G.J. (2008). Quantum Information. Quantum Optics, Springer.","DOI":"10.1007\/978-3-540-28574-8"},{"key":"ref_27","unstructured":"Carmichael, H. (2009). An Open Systems Approach to Quantum Optics: Lectures Presented at the Universit\u00e9 Libre de Bruxelles, October 28 to November 4, 1991, Springer Science & Business Media."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2689","DOI":"10.1109\/TNSM.2022.3165202","article-title":"Eavesdropping detection in BB84 quantum key distribution protocols","volume":"19","author":"Lee","year":"2022","journal-title":"IEEE Trans. Netw. Serv. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wilde, M. (2013). Quantum Information Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781139525343"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Petersen, I. (2013). Control of Quantum Systems. Encyclopedia of Systems and Control, Springer.","DOI":"10.1007\/978-1-4471-5102-9_147-1"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum Cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1364\/AOP.361502","article-title":"Advances in Quantum Cryptography","volume":"12","author":"Pirandola","year":"2020","journal-title":"Adv. Opt. Photonics"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"113026","DOI":"10.1088\/1367-2630\/12\/11\/113026","article-title":"Experimental Demonstration of Phase-Remapping Attack in a Practical Quantum Key Distribution System","volume":"12","author":"Xu","year":"2020","journal-title":"New J. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1038\/nphoton.2014.149","article-title":"Secure Quantum Key Distribution","volume":"8","author":"Lo","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_35","unstructured":"Steven, M.K. (1993). Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory, PTR Prentice-Hall. Available online: https:\/\/www.pearson.com\/en-us\/subject-catalog\/p\/fundamentals-of-statistical-processing-estimation-theory-volume-1\/P200000009271\/9780133457117?srsltid=AfmBOooCqGCXfEcX9V9e80-7ys_yLjY4XEpNcR03OYSXdl6lEhgwdwkA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Song, Z., Chen, Y., Sastry, C.R., and Tas, N.C. (2009). Optimal Observation for Cyber-Physical Systems: A Fisher-Information-Matrix-Based Approach, Springer Science & Business Media.","DOI":"10.1007\/978-1-84882-656-4"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012107","DOI":"10.1103\/PhysRevA.62.012107","article-title":"Quantum properties of classical Fisher information","volume":"62","author":"Hall","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Petz, D., and Ghinea, C. (2011). Introduction to quantum Fisher information. Quantum Probability and Related Topics, World Scientific.","DOI":"10.1142\/9789814338745_0015"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1142\/S0219749909004839","article-title":"Quantum estimation for quantum technology","volume":"7","author":"Paris","year":"2009","journal-title":"Int. J. Quantum Inf."},{"key":"ref_40","unstructured":"Shostack, S. (2025, April 07). The Ultimate Beginner\u2019s Guide to Threat Modeling. Available online: https:\/\/shostack.org\/resources\/threat-modeling.html."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/MSP.2004.111","article-title":"Static analysis for security","volume":"2","author":"Chess","year":"2004","journal-title":"IEEE Secur. 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