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Published June 2021 | Submitted + Published
Journal Article Open

Thermodynamic Implementations of Quantum Processes

Abstract

Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

Additional Information

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Received 15 November 2019; Accepted 28 April 2021; Published 28 May 2021. The authors thank Álvaro Alhambra, David Ding, Patrick Hayden, Rahul Jain, David Jennings, Martí Perarnau-Llobet, Mark Wilde, and Andreas Winter for discussions. PhF acknowledges support from the Swiss National Science Foundation (SNSF) through the Early PostDoc.Mobility Fellowship No. P2EZP2_165239 hosted by the Institute for Quantum Information and Matter (IQIM) at Caltech, from the IQIM which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907), from the Department of Energy Award DE-SC0018407, from the Swiss National Science Foundation (SNSF) through the NCCR QSIT and through Project No. 200020_16584, and from the Deutsche Forschungsgemeinschaft (DFG) Research Unit FOR 2724. FB is supported by the NSF. This work was completed prior to MB and FB joining the AWS Center for Quantum Computing. Open Access funding enabled and organized by Projekt DEAL.

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Published - Faist2021_Article_ThermodynamicImplementationsOf.pdf

Submitted - 1911.05563.pdf

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Additional details

Created:
August 20, 2023
Modified:
October 23, 2023