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Computation in sofie quantum dynamical systems

Karoline Wiesner, James P. Crutchfield

Published Dec 1, 2007• 0 citations
OpenAlex

Abstract

We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.

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We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.
We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.
Nature intrinsically computes. It has been suggested that the entire universe is a computer, in particular, a quantum computer. To corroborate this idea we require tools to quantify the information processing. Here we review a theoretical framework for quantifying information processing in a quantum dynamical system. So-called intrinsic quantum computation combines tools from dynamical systems theory, information theory, quantum mechanics, and computation theory. We will review how far the framework has been developed and what some of the main open questions are. On the basis of this framework we discuss upper and lower bounds for intrinsic information storage in a quantum dynamical system.
In this work, we use the theory of quantum states over time to define joint entropy for timelike-separated quantum systems. For timelike-separated systems that admit a dual description as being spacelike-separated, our notion of entropy recovers the usual von Neumann entropy for bipartite quantum states and thus may be viewed as a spacetime generalization of von Neumann entropy. Such an entropy is then used to define dynamical extensions of quantum joint entropy, quantum conditional entropy, and quantum mutual information for systems separated by the action of a quantum channel. We provide an in-depth mathematical analysis of such information measures and the properties they satisfy. We also use such a dynamical formulation of entropy to quantify the information loss/gain associated with the dynamical evolution of quantum systems, which enables us to formulate a precise notion of information conservation for quantum processes. Finally, we show how our dynamical entropy admits an operational interpretation in terms of quantifying the amount of state disturbance associated with a positive operator- valued measurement.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a unique opportunity for information processing. This paper explores the theoretical framework for quantifying and manipulating this entangled state, ultimately aiming to understand its implications for quantum computation and information theory. We propose a novel entropy calculation model rooted in entangled states, linking this process directly with established mathematical expressions of information entropy. This research delves into the potential for leveraging entanglement for enhanced quantum information storage and efficient computation, highlighting a potential paradigm shift in this field. The study considers the interplay between entanglement, information theory, and the limitations of classical computation.
This paper investigates the potential of quantum chaotic systems to store information entropy. We propose a framework leveraging the inherent complexity of chaotic states in quantum systems to facilitate information storage. The core concept involves mapping the dynamics of a quantum chaotic system to represent and preserve information, drawing parallels between the storage capacity of chaos and the concept of entropy. We explore theoretical formulations of this approach, focusing on the relationship between the system's parameters, the generated chaotic behavior, and the resulting information storage capacity. Our work aims to contribute to the burgeoning field of quantum information storage and potentially illuminate the fundamental connection between chaos and information processing. The methodology presented allows for a novel approach to information storage using quantum phenomena, offering a theoretical foundation for future research and development. The core claim is the utilization of quantum chaotic states to achieve information entropy storage, while the core mechanism involves combining the complexity of chaotic states with the storage capabilities of entropy. ---
We establish a direct connection between quantum thermodynamics and information geometry by introducing an ergotropic decomposition of the Wigner-Fisher information for Gaussian quantum states. We derive an analytical expression for the Wigner-Fisher information in terms of the phase-space covariance matrix and mean vector, and show that it naturally separates into passive and ergotropic contributions. The passive term is shown to be entirely determined by the Wigner entropy rate of the associated passive state. The ergotropic contribution, in turn, quantifies how displacement and squeezing resources modify the statistical velocity and length of the system trajectory in phase space. As an application, we analyze the recently proposed ergotropic Mpemba effect and demonstrate that it can be traced to the anomalous geometric evolution of the passive state associated with squeezed thermal states. Our results reveal how the extractable work stored in a quantum state constrains its information-geometric structure, establishing a framework that links ergotropy, entropy production rate, and statistical geometry in continuous-variable quantum systems.