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arXiv:1407.7765 · Physical Review X

Extractable Work from Correlations

Martí Perarnau-Llobet, Karen V. Hovhannisyan, Marcus Huber, Paul Skrzypczyk, Nicolas Brunner, Antonio Acín

Published Oct 22, 2015• 269 citations
arXivHTMLPDF

Abstract

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory.In this work, we study how to use correlations among quantum systems to optimally store work.We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems.We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations.We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy.Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.

DOI
10.1103/physrevx.5.041011

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Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory.In this work, we study how to use correlations among quantum systems to optimally store work.We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems.We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations.We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy.Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.
We consider the problem of extracting work from isolated quantum systems composed of nnn subsystems. In this scenario the work can be naturally divided into two contributions: a local contribution from each subsystem, and a global contribution originating from correlations between subsystems. Here we focus on the latter and consider quantum systems which are locally thermal, thus from which work can only be extracted from correlations. We derive bounds on the extractable work for general quantum states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum systems, this gain vanishes for a large number of subsystems.
We establish a rigorous connection between fundamental resource theories at the quantum scale. Correlations and entanglement constitute indispensable resources for numerous quantum information tasks. However, their establishment comes at the cost of energy, the resource of thermodynamics, and is limited by the initial entropy. Here, the optimal conversion of energy into correlations is investigated. Assuming the presence of a thermal bath, we establish general bounds for arbitrary systems and construct a protocol saturating them. The amount of correlations, quantified by the mutual information, can increase at most linearly with the available energy, and we determine where the linear regime breaks down. We further consider the generation of genuine quantum correlations, focusing on the fundamental constituents of our universe: fermions and bosons. For fermionic modes, we find the optimal entangling protocol. For bosonic modes, we show that while Gaussian operations can be outperformed in creating entanglement, their performance is optimal for high energies.
It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the egrotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.
We investigate the dynamics of quantum ergotropy in a multipartite system of two-level atoms interacting with a quantized field. The role of multipartite quantum mutual information and quantum relative entropy is analyzed to understand how correlations and the distinguishability between the passive state and the product of local states affect the extractable work. Numerical results for systems containing two to five atoms show that the maximum ergotropy does not increase linearly with the system size, while the intervals of zero ergotropy are gradually modified and suppressed for larger systems. We also study the effect of the average thermal photon number and different initial atomic states. Increasing the thermal photon number mainly reduces the relative-entropy contribution, whereas the initial state strongly influences both the magnitude and persistence of ergotropy. Among the considered states, the partially entangled state provides the largest and more persistent extractable work, while the mixed GHZ state gives the smallest ergotropy. These results highlight the importance of multipartite correlations, thermal effects, and state preparation in controlling quantum work extraction and may be useful for future studies of quantum batteries and quantum power.
Inspired by the primary goal of quantum thermodynamics-to characterize quantum signatures and leverage their benefits in thermodynamic scenarios-we design a work extraction task within a bipartite framework that exhibits a quantum thermodynamic advantage. The steerability of quantum correlations between the two parties is the key resource enabling such an advantage. In designing the task, we exploit the correspondence between steerability and the incompatibility of observables. Our work extraction protocol involves mutually unbiased bases, which exhibit maximum incompatibility and therefore maximum steerability, showcased in maximally entangled quantum states. The work extraction protocols consist of quenches and thermalization processes, which serve as fundamental building blocks for various thermodynamic protocols, such as heat engines. We derive upper bounds on the extractable work for unsteerable and steerable correlations and devise a protocol that saturates the latter. The ratio between the extractable work in steerable and unsteerable scenarios, which encapsulates the quantum advantage, increases with the dimension of the underlying system (sometimes referred to as an unbounded advantage). This proves a quantum thermodynamic advantage arising from steerable quantum correlations.
Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord, and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, whereas total, classical, and entanglement correlations can reduce the work extraction.