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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. In: 2014 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 331-335. ISBN 978-1-4799-5186-4. http://resolver.caltech.edu/CaltechAUTHORS:20150227-081211253

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Abstract

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 [Winter, CMP 244 (157), 2004] 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. Our proof is based on quantum-proof randomness extractors and the post-selection technique for quantum channels [Christandl et al., PRL 102 (020504), 2009].


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2014.6874849DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6874849PublisherArticle
http://arxiv.org/abs/1301.1594arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Additional Information:© 2014 IEEE. We acknowledge discussions with Francesco Buscemi, Matthias Christandl, Patrick Hayden, and Marco Tomamichel. MMW acknowledges support from the Centre de Recherches Mathématiques at the University of Montreal.
Group:IQIM, Institute for Quantum Information and Matter
Record Number:CaltechAUTHORS:20150227-081211253
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150227-081211253
Official Citation:Berta, M.; Renes, J.M.; Wilde, M.M., "Identifying the information gain of a quantum measurement," Information Theory (ISIT), 2014 IEEE International Symposium on , vol., no., pp.331,335, June 29 2014-July 4 2014 doi: 10.1109/ISIT.2014.6874849 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6874849&isnumber=6874773
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55315
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 Mar 2015 00:09
Last Modified:17 Aug 2017 00:02

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