A Caltech Library Service

Thermodynamic Implementations of Quantum Processes

Faist, Philippe and Berta, Mario and Brandão, Fernando G. S. L. (2021) Thermodynamic Implementations of Quantum Processes. Communications in Mathematical Physics, 384 (3). pp. 1709-1750. ISSN 0010-3616. PMCID PMC8550554. doi:10.1007/s00220-021-04107-w.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription CentralArticle Paper
Faist, Philippe0000-0003-1696-6400
Berta, Mario0000-0002-0428-3429
Brandão, Fernando G. S. L.0000-0003-3866-9378
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 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.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)P2EZP2_165239
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Swiss National Science Foundation (SNSF)200020_16584
Deutsche Forschungsgemeinschaft (DFG)FOR 2724
Issue or Number:3
PubMed Central ID:PMC8550554
Record Number:CaltechAUTHORS:20210512-104034146
Persistent URL:
Official Citation:Faist, P., Berta, M. & Brandao, F.G.S.L. Thermodynamic Implementations of Quantum Processes. Commun. Math. Phys. 384, 1709–1750 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109095
Deposited By: George Porter
Deposited On:12 May 2021 19:42
Last Modified:12 Nov 2021 17:24

Repository Staff Only: item control page