Gaussian work extraction from random Gaussian states is nearly impossible

• URL: http://arxiv.org/abs/2212.03492v2
• Date: Tue, 18 Jul 2023 10:21:23 GMT
• Title: Gaussian work extraction from random Gaussian states is nearly impossible
• Authors: Uttam Singh, Jaros{\l}aw K. Korbicz, Nicolas J. Cerf
• Abstract summary: A key resource in thermodynamics is the extractable work, forming the backbone of thermal engines. We show that Gaussian states are typically useless for Gaussian work extraction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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