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Quantum Information and Measurement (QIM)

Extracting work from quantum measurement in Maxwell demon engines

Cyril Elouard, David A. Herrera-Martí, Benjamin Huard, Alexia Auffèves

Published Jan 1, 2017• 4 citations
Publisher

Abstract

We propose a new type of Maxwell demon engine where the work is directly extracted from the measurement channel, requiring no heat bath. In the regime of frequent measurements, memory erasure costs eventually vanish.
DOI
10.1364/qim.2017.qw5b.4

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Extracting Work from Quantum Measurement in Maxwell’s Demon Engines

Cyril Elouard, David A. Herrera-Martí, Benjamin Huard +1 more

The essence of both classical and quantum engines is to extract useful energy (work) from stochastic energy sources, e.g., thermal baths. In Maxwell's demon engines, work extraction is assisted by a feedback control based on measurements performed by a demon, whose memory is erased at some nonzero energy cost. Here we propose a new type of quantum Maxwell's demon engine where work is directly extracted from the measurement channel, such that no heat bath is required. We show that in the Zeno regime of frequent measurements, memory erasure costs eventually vanish. Our findings provide a new paradigm to analyze quantum heat engines and work extraction in the quantum world.

arXiv:1702.01917•Physical Review Letters•Jun 29, 2017•214 citations
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.
We propose quantum engines powered entirely by a position-resolving measurement performed on a quantum particle. These engines produce work by moving the quantum particle against a force. Unlike classical information-driven engines (e.g., Maxwell's demon), the energy is not extracted from a thermal hot source but directly from the observation process via a partial wave-function collapse of the particle. We present results for the work done and the efficiency for different values of the engine parameters. Feedback is required for optimal performance. We find that unit efficiency can be approached when one measurement outcome prepares the initial state of the next engine cycle, while the other outcomes leave the original state nearly unchanged.
Quantum measurement of a system can change its mean energy, as well as entropy. A selective measurement (classical or quantum) can be used as a "Maxwell's demon" to power a single-temperature heat engine, by decreasing the entropy. Quantum mechanically, so can a non-selective measurement, despite increasing the entropy of a thermal state. The maximal amount of work extractable following the measurement is given by the change in free energy: Wmax(non−)sel.=ΔEmeas−TBathΔSmeas(non−)sel.W_{max}^{(non-)sel.}=ΔE_{meas}-T_{Bath}ΔS_{meas}^{(non-)sel.}Wmax(non−)sel.​=ΔEmeas​−TBath​ΔSmeas(non−)sel.​. This follows from the "generalized 2nd law for nonequilibrium initial state" [Hasegawa et. al, PLA (2010)], of which an elementary reduction to the standard law is given here. It is shown that Wmaxsel.−Wmaxnon−sel.W_{max}^{sel.}-W_{max}^{non-sel.}Wmaxsel.​−Wmaxnon−sel.​ equals the work required to reset the memory of the measuring device, and that no such resetting is needed in the non-selective case. Consequently, a single-bath engine powered by either kind of measurement works at a net loss of TBathΔSmeasnon−selT_{Bath}ΔS_{meas}^{non-sel}TBath​ΔSmeasnon−sel​ per cycle. By replacing the measurement by a reversible "premeasurement" and allowing a work source to couple to the system and memory, the cycle can be made completely reversible.
The essence of both classical and quantum engines is to extract useful energy (work) from stochastic energy sources, e.g., thermal baths. In Maxwell's demon engines, work extraction is assisted by a feedback control based on measurements performed by a demon, whose memory is erased at some nonzero energy cost. Here we propose a new type of quantum Maxwell's demon engine where work is directly extracted from the measurement channel, such that no heat bath is required. We show that in the Zeno regime of frequent measurements, memory erasure costs eventually vanish. Our findings provide a new paradigm to analyze quantum heat engines and work extraction in the quantum world.