Gaussian work extraction from random Gaussian states is nearly impossible

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. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.