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Fluctuations in measurement-based quantum engines and quantum batteries derived from the Kirkwood-Dirac quasiprobability distribution

Abdelkader El Makouri1,*, Abdallah Slaoui1,2, and Rachid Ahl Laamara1,2

  • *Contact author: abdelkader_elmakouri@um5.ac.ma
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APS Open Sci. 1, 000020 – Published 12 May, 2026

DOI: https://doi.org/10.1103/fls6-mxgq

Abstract

In this paper, we consider fluctuations in a three-stroke cycle based on quantum measurement. In the first stroke, the engine is fueled by a nonselective quantum measurement; in the second stroke, an appropriate unitary operation is applied to extract work; and finally, the working medium is thermalized to complete the cycle. This protocol is analogous to charging, then discharging, and finally thermalizing a quantum battery. Using the Kirkwood-Dirac quasiprobability, we derive equations that provide insights into the fluctuations of heat and work, and thus into the charging and discharging processes. We then propose a quantum circuit to measure the cumulants of work and heat using a qubit ancilla. Afterward, we derive important upper and lower bounds on fluctuations in heat; this is thanks to the way we decompose heat fluctuations and the Kadison-Schwarz inequality. We also show, for the first time, that the imaginary part of the second cumulant of work equals the linear response of an average work (to be defined in the main text) or the quantum cross entropy. We further introduce an operator whose average defines the battery capacity and whose variance quantifies the corresponding fluctuations of the battery capacity. Our analytical results are illustrated and discussed through representative examples. We believe that our study will, on the one hand, be useful for understanding fluctuations in energy extracted from and injected into quantum batteries based on quantum measurements and, on the other hand, contribute to the foundations of quantum thermodynamics. More generally, our results can be applied beyond the three-stroke cycle considered here, especially to quantum batteries subject to environmental noise and decoherence.

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Outline

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APS Open Sci. 1, 000020– Published 12 May, 2026
Vol. 1
  • Received 24 September 2025
  • Revised 3 February 2026
  • Accepted 20 March 2026
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