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Rényi generalizations of quantum information measures

Berta, Mario and Seshadreesan, Kaushik P. and Wilde, Mark M. (2015) Rényi generalizations of quantum information measures. Physical Review A, 91 (2). Art. No. 022333. ISSN 1050-2947. https://resolver.caltech.edu/CaltechAUTHORS:20150402-141635172

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Abstract

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the Rényi entropies is expected to enhance their scope in applications. We prescribe Rényi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {−1,0,1} . As examples, we describe Rényi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the Rényi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed Rényi conditional quantum mutual informations are monotone increasing in the Rényi parameter, and we have proof of this conjecture for some special cases.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevA.91.022333DOIArticle
http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.022333PublisherArticle
http://arxiv.org/abs/1502.07977arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Additional Information:© 2015 American Physical Society. Received 13 August 2014; revised manuscript received 23 December 2014; published 27 February 2015. M.B. is grateful for the hospitality of the Hearne Institute for Theoretical Physics and the Department of Physics and Astronomy at LSU for hosting him as a visitor during March 2014, when some of the research in this paper was completed. K.S. acknowledges support from the Army Research Office and NSF Grant No. CCF-1350397. M.M.W. acknowledges startup funds from the Department of Physics and Astronomy at LSU, support from the NSF under Award No. CCF-1350397, and support from the DARPA Quiness Program through US Army Research Office Award No. W31P4Q-12-1-0019.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1350397
Louisiana State University (LSU)UNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Army Research Office (ARO)W31P4Q-12-1-0019
Issue or Number:2
Classification Code:PACS: 03.67.Mn
Record Number:CaltechAUTHORS:20150402-141635172
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150402-141635172
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56316
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Apr 2015 21:28
Last Modified:03 Oct 2019 08:13

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