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arXiv:quant-ph/0311083 · Physical Review A

Thermodynamical detection of entanglement by Maxwell’s demons

Koji Maruyama, Fumiaki Morikoshi, Vlatko Vedral

Published Jan 31, 2005• 40 citations
arXivHTMLPDF

Abstract

Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing, what kind of physical processes can exploit entanglement? In this paper, we show that there is indeed a more basic relationship between entanglement and its usefulness in thermodynamics. We derive an inequality showing that we can extract more work out of a heat bath via entangled systems than via classically correlated ones. We also analyze the work balance of the process as a heat engine, in connection with the second law of thermodynamics.

DOI
10.1103/physreva.71.012108

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Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing, what kind of physical processes can exploit entanglement? In this paper, we show that there is indeed a more basic relationship between entanglement and its usefulness in thermodynamics. We derive an inequality showing that we can extract more work out of a heat bath via entangled systems than via classically correlated ones. We also analyze the work balance of the process as a heat engine, in connection with the second law of thermodynamics.
Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing, what kind of physical processes can exploit entanglement? In this Letter, we show that there is indeed a more basic relationship between entanglement and its usefulness in thermodynamics by illustrating that we can extract more work out of entangled systems than out of classically correlated ones. Our results suggest a novel connection between entanglement and thermodynamics.
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.
Abstract We identify that quantum coherence is a valuable resource in the quantum heat engine, which is designed in a quantum thermodynamic cycle assisted by a quantum Maxwell’s demon. This demon is in a superposed state. The quantum work and heat are redefined as the sum of coherent and incoherent parts in the energy representation. The total quantum work and the corresponding efficiency of the heat engine can be enhanced due to the coherence consumption of the demon. In addition, we discuss an universal information heat engine driven by quantum coherence. The extractable work of this heat engine is limited by the quantum coherence, even if it has no classical thermodynamic cost. This resource-driven viewpoint provides a direct and effective way to clarify the thermodynamic processes where the coherent superposition of states cannot be ignored.
In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.
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.
Within the framework of microscopic thermodynamics, correlations can play a crucial role for energy extraction. Our work sheds light on this connection by demonstrating that entanglement governs the amount of extractable energy in a controllable setting. We experimentally investigate a fundamental link between information, encoded in tunable non-classical correlations and quantified by quantum state tomography, and its utility as fuel for energy extraction. We realize an agent-demon protocol involving two trapped-ion qubits, and show that by implementing an appropriate feedback policy, the demon can optimize the energy extraction process, capitalizing on the correlations between the system's constituents. By quantifying both the concurrence of the two-qubit resource state and the energy extraction gain from applying the feedback policy, we corroborate the connection between information and energy, solidifying the role of non-classical correlations as a resource for thermodynamic processes.