Quantum Theoretical Methods in Application to Classical Systems

Jian Chun Wu

Riddhi Swaroop Gupta, Michael J. Biercuk

The authors discuss the application of classical filtering techniques to the problem of discrete projective measurements in quantum systems, and demonstrate that the theoretical basis of classical nonlinear filtering applies in this context. The results may pave the way for broader adoption of control-theoretic techniques in quantum technology.

Shiro Ishikawa, Kohshi Kikuchi

Recently we proposed quantum language(or, measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. Also, we consider that this is a kind of system theory such that it is applicable to both classical and quantum systems. As far as classical systems, it should be noted that quantum language is similar to statistics. In this paper, we discuss the usual confidence interval methods in terms of quantum language. And we assert that three concepts (i.e.,"estimator" and "quantity" and "semi-distance)are indispensable for the theoretical understanding of the confidence interval methods. Since our argument is quite elementary, we hope that the readers acquire a new viewpoint of statistics, and agree that our proposal is, from the pure theoretical point of view, the true confidence interval methods. (Key words: Confidence interval, Chi-squared distribution, Student's t-distribution)

Pavel Bóna

Sarah Chehade, Joel Dawson, Stacy Prowell +1 more

Hybrid quantum-classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum-classical interface (QCI)-the boundary enabling these systems-introduces 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-including quantum key distribution, quantum sensing, and hybrid control systems-we 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.