Gaussian work extraction from random Gaussian states is nearly impossible

TL;DR

This paper demonstrates that extracting work from random Gaussian states in quantum thermodynamics is nearly impossible, highlighting a fundamental limitation of Gaussian states in quantum energy transfer processes.

Contribution

It proves that the probability of nonzero work extraction from random Gaussian states is exponentially small, establishing an $ ext{epsilon}$-no-go theorem for Gaussian work extraction.

Findings

Gaussian states are generally ineffective for work extraction.

The probability of extracting nonzero work is exponentially small.

Gaussian components have fundamental limitations in quantum thermodynamics.

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 $\epsilon$-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.