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Physical Review A

Detailed fluctuation theorem from the one-time measurement scheme

Kenji Maeda, Tharon Holdsworth, Sebastian Deffner, Akira Sone

Published Nov 17, 2023• 6 citations
Publisher

Abstract

The authors develop a quantum fluctuation theorem from quantum nondemolition measurements, considering the influence of quantum coherence and correlations. They demonstrate that the derived fluctuation theorem captures detailed information about the irreversibility of the quantum process, which can be useful for quantum thermometry.
DOI
10.1103/physreva.108.l050203

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The quantum fluctuation theorem can be regarded as the first principle of quantum nonequilibrium thermodynamics. However, many different formulations have been proposed, which depend on how quantum work is defined. In this context, we have seen that for some situations the one-time measurement (OTM) scheme can be more informative than the two-time measurement (TTM) scheme. Yet, so far the focus of OTM has been on integral fluctuation theorems, since, the work distribution of the backward process has been lacking. To this end, we prove that the OTM scheme is the nondestructive TTM scheme, in which the final state is a pointer state of the second measurement whose Hamiltonian is conditioned on the first measurement outcome. This insight leads to a derivation of the detailed fluctuation theorem for the characteristic functions of the forward and backward work distributions. Finally, our conceptual findings are experimentally verified with the IBM quantum computer.
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.
Fluctuation theorems are relations constraining the out-of-equilibrium fluctuations of thermodynamic quantities like the entropy production that were initially introduced for classical or quantum systems in contact with a thermal bath. Here we show, in the absence of thermal bath, the dynamics of continuously measured quantum systems can also be described by a fluctuation theorem, expressed in terms of a recently introduced arrow of time measure. This theorem captures the emergence of irreversible behavior from microscopic reversibility in continuous quantum measurements. From this relation, we demonstrate that measurement-induced wave-function collapse exhibits absolute irreversibility, such that Jarzynski-like equalities are violated, and that this property is inherent to quantum information acquisition. We apply our results to different continuous measurement schemes on a qubit: dispersive measurement, homodyne, and heterodyne detection of qubit's fluorescence.
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the statistical behaviour of thermodynamic systems far from equilibrium, are now well established. Their quantum counterparts, however, remain an active area of research. In this review, we highlight recent advances by linking quantum fluctuation theorems with linear response theory, offering new insights into the nature of quantum fluctuations and irreversibility in the near-equilibrium regime. Particular emphasis is placed on dissipated work in quantum systems as a pathway to observing non-classical effects in quantum thermodynamics. Understanding quantum fluctuations is not only essential for clarifying the foundations of irreversibility but also crucial for the development of novel quantum technologies, including quantum computers, sensors, and metrological devices.
Abstract Information spreads in time. For example, correlations dissipate when the correlated system locally couples to a third party, such as the environment. This simple but important fact forms the known quantum data-processing inequality. Here we theoretically uncover the quantum fluctuation theorem behind the quantum informational inequality. The fluctuation theorem quantitatively predicts the statistics of the underlying stochastic quantum process. To fully capture the quantum nature, the fluctuation theorem established here is extended to the quasiprobability regime. We also experimentally apply an interference-based method to measure the amplitudes composing the quasiprobability and verify our established fluctuation theorem by the IBM quantum computer.
In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of a closed system environment. The assumption that the system evolves under a completely positive and trace-preserving map is quite general, but it is more specific for cases in which the system is initially correlated with the environment. System-environment correlations arise naturally in multitime processes with which we can give clear and physical interpretations regarding the effects of correlations. Multitime processes can provide many-body channels. The Choi state of such a many-body channel is called a process tensor. One can derive channels by executing the process tensor on a set of operations. We establish a general quantum fluctuation theorem framework for a many-body channel and its derived channels. In this framework, the effects of correlations are reflected in a Markovian property. For Markovian processes, we can extend the two-point measurement to a three-point measurement and obtain that the fluctuation theorems contain complete information about the intermediate state. For non-Markovian processes, the complete measurement of the intermediate state leads to conflicts. Therefore, we use a general measurement, which only provides partial information, for the intermediate state. The corresponding fluctuation theorems show that memory effects can reduce these fluctuations. This is consistent with the fact that system states can be recovered under non-Markovian processes.