Conditional work statistics of quantum measurements

M. Hamed Mohammady; Alessandro Romito

doi:10.22331/q-2019-08-19-175

Conditional work statistics of quantum measurements

M. Hamed Mohammady^1,2 and Alessandro Romito¹

¹Department of Physics, Lancaster University, LA1 4YB, United Kingdom
²RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia

Published:	2019-08-19, volume 3, page 175
Eprint:	arXiv:1809.09010v6
Doi:	https://doi.org/10.22331/q-2019-08-19-175
Citation:	Quantum 3, 175 (2019).

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Abstract

In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energy before the measurement process is shown to be given by the real component of the weak value of the Hamiltonian. Our definition generalises well-known notions of distributions of internal energy change, such as that given by stochastic thermodynamics. By determining the conditional energy change of both system and measurement apparatus, we obtain the full conditional work statistics of quantum measurements, and show that this vanishes for all measurement outcomes if the measurement process conserves the total energy. Additionally, by incorporating the measurement process within a cyclic heat engine, we quantify the non-recoverable work due to measurements. This is shown to always be non-negative, thus satisfying the second law, and will be independent of the apparatus specifics for two classes of projective measurements.

► BibTeX data

@article{Mohammady2019conditionalwork,
  doi = {10.22331/q-2019-08-19-175},
  url = {https://doi.org/10.22331/q-2019-08-19-175},
  title = {Conditional work statistics of quantum measurements},
  author = {Mohammady, M. Hamed and Romito, Alessandro},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {175},
  month = aug,
  year = {2019}
}

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[2] M. Hamed Mohammady, "Classicality of the heat produced by quantum measurements", Physical Review A 104 6, 062202 (2021).

[3] Leon Loveridge, "A relational perspective on the Wigner-Araki-Yanase theorem", Journal of Physics: Conference Series 1638 1, 012009 (2020).

[4] Quancheng Liu, Klaus Ziegler, David A. Kessler, and Eli Barkai, "Driving quantum systems with periodic conditional measurements", Physical Review Research 4 2, 023129 (2022).

[5] Giulia Rubino, Gonzalo Manzano, and Časlav Brukner, "Quantum superposition of thermodynamic evolutions with opposing time’s arrows", Communications Physics 4 1, 251 (2021).

[6] M Hamed Mohammady, "Thermodynamically free quantum measurements", Journal of Physics A: Mathematical and Theoretical 55 50, 505304 (2022).

[7] Yuxia Zhang, Jian Zou, and Bin Shao, "No-Signaling-in-Time (NSIT) Condition for Energy", Entropy 21 11, 1067 (2019).

[8] Mohammad Mehboudi and Harry J. D. Miller, "Thermodynamic length and work optimization for Gaussian quantum states", Physical Review A 105 6, 062434 (2022).

[9] J. Stevens, D. Szombati, M. Maffei, C. Elouard, R. Assouly, N. Cottet, R. Dassonneville, Q. Ficheux, S. Zeppetzauer, A. Bienfait, A. N. Jordan, A. Auffèves, and B. Huard, "Energetics of a Single Qubit Gate", Physical Review Letters 129 11, 110601 (2022).

[10] M. H. Mohammady, A. Auffèves, and J. Anders, "Energetic footprints of irreversibility in the quantum regime", Communications Physics 3 1, 89 (2020).

[11] Gabriel T. Landi, Mauro Paternostro, and Alessio Belenchia, "Informational Steady States and Conditional Entropy Production in Continuously Monitored Systems", PRX Quantum 3 1, 010303 (2022).

[12] Alessio Belenchia, Mauro Paternostro, and Gabriel T. Landi, "Informational steady states and conditional entropy production in continuously monitored systems: The case of Gaussian systems", Physical Review A 105 2, 022213 (2022).

[13] M. Hamed Mohammady and Alessandro Romito, "Symmetry constrained decoherence of conditional expectation values", arXiv:1901.01460, (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 14:09:32) and SAO/NASA ADS (last updated successfully 2023-05-29 14:09:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

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