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Identifying the Information Gain of a Quantum Measurement

Berta, Mario and Renes, Joseph M. and Wilde, Mark M. (2014) Identifying the Information Gain of a Quantum Measurement. IEEE Transactions on Information Theory, 60 (12). pp. 7987-8006. ISSN 0018-9448. doi:10.1109/TIT.2014.2365207.

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We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs to arbitrary inputs, and more importantly, it identifies the quantum mutual information of a measurement as the information gained by performing it, independent of the input state on which it is performed. Our result is a generalization of the classical reverse Shannon theorem to quantum-to-classical channels. In this sense, it can be seen as a quantum reverse Shannon theorem for quantum-to-classical channels, but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication, respectively. The proof is based on a novel one-shot state merging protocol for classically coherent states as well as the postselection technique for quantum channels, and it uses techniques developed for the quantum reverse Shannon theorem.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle Paper
Berta, Mario0000-0002-0428-3429
Wilde, Mark M.0000-0002-3916-4462
Additional Information:© 2014 IEEE. Manuscript received January 28, 2014; revised August 9, 2014; accepted October 18, 2014. Date of publication October 31, 2014; date of current version November 18, 2014. J. M. Renes was supported in part by the Swiss National Science Foundation through the National Centre of Competence in Research Quantum Science and Technology and in part by the European Research Council under Grant 258932. M. M. Wilde was supported in part by the Centre de Recherches Mathématiques and in part by the University of Montréal, Montréal, QC, Canada. The authors acknowledge discussions with Francesco Buscemi, Matthias Christandl, Nilanjana Datta, Patrick Hayden, Renato Renner, and Marco Tomamichel.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
European Research Council (ERC)258932
Centre de Recherches MathématiquesUNSPECIFIED
University of MontréalUNSPECIFIED
Subject Keywords:Quantum measurement; measurement compression; reverse Shannon theorem; channel simulation; quantum Shannon theory
Issue or Number:12
Record Number:CaltechAUTHORS:20150106-105223454
Persistent URL:
Official Citation:Berta, M.; Renes, J.M.; Wilde, M.M., "Identifying the Information Gain of a Quantum Measurement," Information Theory, IEEE Transactions on , vol.60, no.12, pp.7987,8006, Dec. 2014 doi: 10.1109/TIT.2014.2365207 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53206
Deposited By: Tony Diaz
Deposited On:06 Jan 2015 19:08
Last Modified:10 Nov 2021 19:49

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