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  • Letter
  • Open Access

Gaussian work extraction from random Gaussian states is nearly impossible

Uttam Singh1,2,3,*, Jarosław K. Korbicz2,†, and Nicolas J. Cerf1,4,‡

  • 1Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium
  • 2Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02-668 Warsaw, Poland
  • 3Centre of Quantum Science and Technology, International Institute of Information Technology, Hyderabad 500032, India
  • 4James C. Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA

  • *uttam@iiit.ac.in
  • †jkorbicz@cft.edu.pl
  • ‡ncerf@ulb.ac.be
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Phys. Rev. Research 5, L032010 – Published 17 July, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032010

Abstract

Quantum thermodynamics can be naturally phrased as a theory of quantum state transformation and energy exchange for small-scale quantum systems undergoing thermodynamical processes, thereby making the resource theoretical approach very well suited. A key resource in thermodynamics is the extractable work, forming the backbone of thermal engines. Therefore it is of interest to characterize quantum states based on their ability to serve as a source of work. From a near-term perspective, quantum optical setups turn out to be ideal test beds for quantum thermodynamics; so it is important to assess work extraction from quantum optical states. Here, we show that Gaussian states are typically useless for Gaussian work extraction. More specifically, by exploiting the “concentration of measure” phenomenon, we prove that the probability that the Gaussian extractable work from a zero-mean energy-bounded multimode random Gaussian state is nonzero is exponentially small. This result can be thought of as an ε-no-go theorem for work extraction from Gaussian states under Gaussian unitaries, thereby revealing a fundamental limitation on the quantum thermodynamical usefulness of Gaussian components.

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Phys. Rev. Research 5, L032010– Published 17 July, 2023
  • Received 7 December 2022
  • Accepted 7 June 2023
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