Theoretical Studies of Classical and Quantum Systems

We sketch a group-theoretical framework, based on the Heisenberg–Weyl group, encompassing both quantum and classical statistical descriptions of unconstrai-ned, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-to-classical transition. We briefly discuss the structure of observables and dynamics within our framework. KEY WORDS: quantum mechanics; classical limit; Heisenberg–Weyl group. 1.We sketch a group-theoretical framework, based on the Heisenberg–Weyl group, encompassing both quantum and classical statistical descriptions of unconstrai-ned, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-to-classical transition. We briefly discuss the structure of observables and dynamics within our framework. KEY WORDS: quantum mechanics; classical limit; Heisenberg–Weyl group. 1.

Jan 1, 20070 citations

A Theoretical Framework for Universal Latency Reduction in Hybrid Quantum-Classical Systems

Aneesh Nandan

Abstract This paper introduces a novel quantum-classical latency reduction formula, representing a theoretical breakthrough in optimizing performance across hybrid systems. Central to our work is \textit{Aneesh Nandan’s Quantum-Classical Latency Reduction Formula}, which models hybrid latency as an exponential function of baseline classical latency and simulated quantum enhancement. The baseline latency ( $L_c$ ) was computed using classical performance metrics—CPU usage, GPU load, and frame rate—measured over a 60-second interval. These data were combined with a simulated range of quantum enhancement values and a noise model to account for experimental variability. The resulting hybrid latencies display a consistent exponential decay as quantum contribution increases, validating the formula’s predictive behavior in theory. To the best of our knowledge, this is the first systematic study to propose a dedicated quantum-classical latency reduction formula, establishing a theoretical framework applicable to domains such as virtual reality, augmented reality, gaming engines, autonomous systems, cloud infrastructure, and quantum-edge computing. All quantum computations were simulated on classical hardware; therefore, the observed latency reductions are theoretical. Future validation using physical quantum systems is necessary to confirm the real-world applicability and effectiveness of this model.Abstract This paper introduces a novel quantum-classical latency reduction formula, representing a theoretical breakthrough in optimizing performance across hybrid systems. Central to our work is \textit{Aneesh Nandan’s Quantum-Classical Latency Reduction Formula}, which models hybrid latency as an exponential function of baseline classical latency and simulated quantum enhancement. The baseline latency ($ L_c $) was computed using classical performance metrics—CPU usage, GPU load, and frame rate—measured over a 60-second interval. These data were combined with a simulated range of quantum enhancement values and a noise model to account for experimental variability. The resulting hybrid latencies display a consistent exponential decay as quantum contribution increases, validating the formula’s predictive behavior in theory. To the best of our knowledge, this is the first systematic study to propose a dedicated quantum-classical latency reduction formula, establishing a theoretical framework applicable to domains such as virtual reality, augmented reality, gaming engines, autonomous systems, cloud infrastructure, and quantum-edge computing. All quantum computations were simulated on classical hardware; therefore, the observed latency reductions are theoretical. Future validation using physical quantum systems is necessary to confirm the real-world applicability and effectiveness of this model.

Nov 4, 20250 citations

Classical and Quantum Physics

R. Asokamani

Elsevier eBooksOct 2, 20260 citations

Entropy of the Quantum–Classical Interface: A Potential Metric for Security

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.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.

EntropyMay 12, 20253 citations

Classical and Quantum Systems: Foundations and Symmetries

H. D. Doebner, Wolfgang Scherer, Franklin E. Schroeck

Jan 1, 199322 citations

L_c

) was computed using classical performance metrics—CPU usage, GPU load, and frame rate—measured over a 60-second interval. These data were combined with a simulated range of quantum enhancement values and a noise model to account for experimental variability. The resulting hybrid latencies display a consistent exponential decay as quantum contribution increases, validating the formula’s predictive behavior in theory. To the best of our knowledge, this is the first systematic study to propose a dedicated quantum-classical latency reduction formula, establishing a theoretical framework applicable to domains such as virtual reality, augmented reality, gaming engines, autonomous systems, cloud infrastructure, and quantum-edge computing. All quantum computations were simulated on classical hardware; therefore, the observed latency reductions are theoretical. Future validation using physical quantum systems is necessary to confirm the real-world applicability and effectiveness of this model.