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arXiv:2102.00777 · New Journal of Physics

Quantum consensus dynamics by entangling Maxwell demon

Sungguen Ryu, Rosa López, Raúl Toral

Published Feb 23, 2022• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ac57ea

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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.
Maxwell's demon explores the role of information in physical processes.Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics.In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion.We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system.The demon is experimentally implemented as a spin-1=2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1=2 system, through a natural interaction.Noise and imperfections in this protocol are investigated by the assessment of its effectiveness.This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
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 $({A}_{1},{A}_{2},\ensuremath{\cdots},{A}_{n})$, 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 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.
Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. They left open the question of whether this bound could be achieved for every measurement that could be made by the controller. We show that it can, and that this follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inform. Dynam. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.
Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. For many quantum measurements their bound was not tight. We show that a tight version of this bound follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inf. Dyn. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.
Information thermodynamics bridges information theory and statistical physics by connecting information content and entropy production through measurement and feedback control. Maxwell's demon is a hypothetical character that uses information about a system to reduce its entropy. Here we realize a Maxwell's demon acting on a superconducting quantum circuit. We implement quantum non-demolition projective measurement and feedback operation of a qubit and verify the generalized integral fluctuation theorem. We also evaluate the conversion efficiency from information gain to work in the feedback protocol. Our experiment constitutes a step toward experimental studies of quantum information thermodynamics in artificially made quantum machines.