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Entanglement preparation and work extraction wiht a truly quantum Maxwell demon

Gang-Gang He, Fulin Zhang

Published Mar 4, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
A Maxwell demon can reduce the entropy of a quantum system by performing measurements on its environment. The nonsignaling theorem prevents the demon from affecting the average state of the system. We study the preparations of quantum correlations from a system qubit and an auxiliary qubit, assisted by a demon who obtains information of the system qubit from measurements on its environment. The demon can affect the postmeasured states of system by choosing different measurements, which establishes the relationships between quantum steering and other correlations in the thermodynamic framework. We present the optimal protocols for creating mutual information, entanglement, and Bell-nonlocality. These maximal correlations are found to relate exactly to the steerable boundary of the system-environment state with maximally mixed marginals. We also present upper bounds of the prepared correlations by utilizing classical environment-system correlation, which can be regarded as steering-type inequalities bounding the correlations created with the aid of classical demons.
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.
Maxwell’s demon is a tiny but fine‐fingered being, capable to extract work from a system at instantaneous equilibrium, without needing energy input or information erasure. In the 20’th century many workers have claimed that the demon cannot operate. Here the point of view is taken that this exorcism of the demon never applied, since one did not consider Maxwell’s original invention. For a Brownian particle coupled to a quantum bath it was shown by us that quantum entanglement can allow extraction of work from a non‐equilibrium system coupled to a single bath. And mesoscopic work sources may establish work extraction cycles even when they are coupled to equilibrium mesoscopic systems immersed in a macroscopic thermal bath. Quantum entanglement and mesocopicity are now identified with (true) Maxwell demons.
We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.
Research of Maxwell demon and quantum entanglement is important because of its foundational significance in physics and its potential applications in quantum information. Previous studies on the Maxwell demon have primarily focused on thermodynamics, taking into account quantum correlations. Here we consider from another perspective and ask whether quantum non-locality correlations can be simulated by performing work. The Maxwell demon-assisted Einstein–Podolsky–Rosen (EPR) steering is thus proposed, which implies a new type of loophole. The application of Landauer’s erasure principle suggests that the only way to close this loophole during a steering task is by continuously monitoring the heat fluctuation of the local environment by the participant. We construct a quantum circuit model of Maxwell demon-assisted EPR steering, which can be demonstrated by current programmable quantum processors, such as superconducting quantum computers. Based on this quantum circuit model, we obtain a quantitative formula describing the relationship between energy dissipation due to the work of the demon and quantum non-locality correlation. The result is of great physical interest because it provides a new way to explore and understand the relationship between quantum non-locality, information, and thermodynamics.