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arXiv:1407.6768 · Physical Review A

Maxwell's demons in multipartite quantum correlated systems

Helena Braga, C. C. Rulli, Thiago Rodrigues de Oliveira, M. S. Sarandy

Published Oct 30, 2014• 13 citations
arXivHTMLPDF

Abstract

We investigate the extraction of thermodynamic work by a Maxwell's demon in a multipartite quantum correlated system. We begin by adopting the standard model of a Maxwell's demon as a Turing machine, either in a classical or quantum setup depending on its ability to implement classical or quantum conditional dynamics. Then, for an $n$-partite system $({A}_{1},{A}_{2},\ensuremath{\cdots},{A}_{n})$, we introduce a protocol of work extraction that bounds the advantage of the quantum demon over its classical counterpart through the amount of multipartite quantum correlation present in the system, as measured by a thermal version of the global quantum discord. This result is illustrated for an arbitrary $n$-partite pure state of qubits with Schmidt decomposition, where it is shown that the thermal global quantum discord exactly quantifies the quantum advantage. Moreover, we also consider the work extraction via mixed multipartite states, where examples of tight upper bounds can be obtained.

DOI
10.1103/physreva.90.042338

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We investigate the extraction of thermodynamic work by a Maxwell's demon in a multipartite quantum correlated system. We begin by adopting the standard model of a Maxwell's demon as a Turing machine, either in a classical or quantum setup depending on its ability to implement classical or quantum conditional dynamics. Then, for an nnn-partite system (A1,A2,\ensuremath⋯,An)({A}_{1},{A}_{2},\ensuremath{\cdots},{A}_{n})(A1​,A2​,\ensuremath⋯,An​), we introduce a protocol of work extraction that bounds the advantage of the quantum demon over its classical counterpart through the amount of multipartite quantum correlation present in the system, as measured by a thermal version of the global quantum discord. This result is illustrated for an arbitrary nnn-partite pure state of qubits with Schmidt decomposition, where it is shown that the thermal global quantum discord exactly quantifies the quantum advantage. Moreover, we also consider the work extraction via mixed multipartite states, where examples of tight upper bounds can be obtained.
Abstract We introduce a Maxwell demon which generates many-body entanglement robustly against bit-flip noises, allowing us to obtain quantum advantage. Adopting the protocol of the voter model used for opinion dynamics approaching consensus, the demon randomly selects a qubit pair and performs a quantum feedback control, in continuous repetitions. We derive upper bounds for the entropy reduction and the work extraction rates by the demon’s operation. These bounds are determined by a competition between the quantum–classical mutual information acquired by the demon and the absolute irreversibility of the feedback control. Our finding of the upper bounds corresponds to a reformulation of the second law of thermodynamics under a class of Maxwell demon which generates many-body entanglement in a working substance. This suggests that a general condition for the operation of a successful entangling demon, one for which many-body entanglement stabilization and work extraction are possible, is that the information gain is larger than the absolute irreversibility.
The information of a quantum system acquired by a Maxwell demon can be used for either work extraction or entanglement preparation. We study these two tasks by using a thermal qubit, in which a demon obtains her information from measurements on the environment of the qubit. The allowed entanglement, between the qubit and an auxiliary system, is enhanced by the information. And, the increment is find to be equivalent to the extractable work. The Maxwell demon is called to be quantum by Beyer \textit{et al.} [Phys. Rev. Lett 123, 250606 (2019) ] if there is quantum steering from the environment to the qubit. In this case, the postmeasured states of the qubit, after the measurements on its environment, cannot be simulated by an objective local statistical ensemble. We present a upper bound of extractable work, and equivalently of the allowed entanglement, for unsteerable demons, considering two measurements inducing two orthogonal changes of the Bloch vector of the qubit.
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.
The emerging field of quantum thermodynamics is beginning to reveal the intriguing role that information can play in quantum thermal engines. Information enters as a resource when considering feedback-controlled thermal machines. While both a general theory of quantum feedback control as well as specific examples of quantum feedback-controlled engines have been presented, still lacking is a general framework for such machines. Here, we present a framework for a generic, two-stroke quantum heat engine interacting with NNN thermal baths and Maxwell's demon. The demon performs projective measurements on the engine working substance, the outcome of which is recorded in a classical memory, embedded in its own thermal bath. To perform feedback control, the demon enacts unitary operations on the working substance, conditioned on the recorded outcome. By considering the compound machine-memory as a hybrid (classical-quantum) standard thermal machine interacting with N+1N+1N+1 thermal baths, our framework puts the working substance and memory on equal footing, thereby enabling a comprehensible resolution to Maxwell's paradox and elucidating the intricate manner in which information impacts the performance of quantum engines. We illustrate the application of our framework with a two-qubit engine. A remarkable observation is that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.