Generalized energy measurements and quantum work compatible with fluctuation theorems

Kosuke Ito, Peter Talkner, B. Prasanna Venkatesh, and Gentaro Watanabe
Phys. Rev. A 99, 032117 – Published 18 March 2019

Abstract

The probability densities of work that can be exerted on a quantum system initially staying in thermal equilibrium are constrained by the fluctuation relations of Jarzynski and Crooks, when the work is determined by two projective energy measurements. We investigate the question whether these fluctuation relations may still hold if one employs generalized energy measurements rather than projective ones. Restricting ourselves to a class of universal measurements which are independent of several details of the system on which the work is done, we find sets of necessary and sufficient conditions for the Jarzynski equality and the Crooks relation. The Jarzynski equality requires perfect accuracy for the initial measurement, while the final one can be erroneous. On the other hand, the Crooks relation can only tolerate a depolarizing channel as a deviation from the projective measurement for systems with a finite-dimensional Hilbert space. For a separable infinite-dimensional space only projective measurements are compatible with the Crooks relation. The results we have obtained significantly extend those of Venkatesh, Watanabe, and Talkner [New J. Phys. 16, 015032 (2014)] as well as avoid some errors present there.

  • Received 18 December 2018

DOI:https://doi.org/10.1103/PhysRevA.99.032117

©2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Kosuke Ito1,*, Peter Talkner2, B. Prasanna Venkatesh3, and Gentaro Watanabe1,4,†

  • 1Department of Physics and Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
  • 2Institut für Physik, Universität Augsburg, Universitätsstraße 1, 86135 Augsburg, Germany
  • 3Indian Institute of Technology, Gandhinagar, Gujarat 382355, India
  • 4Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, Zhejiang 310027, China

  • *kosuke@zju.edu.cn
  • gentaro@zju.edu.cn

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Issue

Vol. 99, Iss. 3 — March 2019

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