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Entropic Uncertainty Relations and their Applications

Coles, Patrick J. and Berta, Mario and Tomamichel, Marco and Wehner, Stephanie (2017) Entropic Uncertainty Relations and their Applications. Reviews of Modern Physics, 89 (1). Art. No. 015002. ISSN 0034-6861. http://resolver.caltech.edu/CaltechAUTHORS:20160622-170348845

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Abstract

Heisenberg’s uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the security analysis of almost all quantum cryptographic protocols, such as quantum key distribution and two-party quantum cryptography. This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements. These ideas are then extended to incorporate quantum correlations between the observed object and its environment, allowing for a variety of recent, more general formulations of the uncertainty principle. Finally, various applications are discussed, ranging from entanglement witnessing to wave-particle duality to quantum cryptography.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/RevModPhys.89.015002DOIArticle
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.89.015002PublisherArticle
https://arxiv.org/abs/1511.04857arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Tomamichel, Marco0000-0001-5410-3329
Additional Information:© 2017 American Physical Society. Published 6 February 2017. We thank Kais Abdelkhalek, Iwo Białynicki-Birula, Matthias Christandl, Rupert L. Frank, Gilad Gour, Michael J. W. Hall, Hans Maassen, Joseph M. Renes, Renato Renner, Lukasz Rudnicki, Christian Schaffner, Reinhard F. Werner, Mark M. Wilde, and Karol Zyczkowski for feedback. P. J. C. acknowledges support from Industry Canada, Sandia National Laboratories, NSERC Discovery Grant, and an Ontario Research Fund (ORF). M. B. acknowledges funding by the Swiss National Science Foundation (SNSF) through a fellowship, funding by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (No. GBMF-12500028), and funding support from the ARO grant for Research on Quantum Algorithms at the IQIM (No. W911NF-12-1-0521). M. T. is funded by a University of Sydney Postdoctoral Fellowship and acknowledges support from the ARC Centre of Excellence for Engineered Quantum Systems (EQUS). S. W. is supported by STW, Netherlands, an ERC Starting Grant QINTERNET, and an NWO VIDI grant.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Industry CanadaUNSPECIFIED
Sandia National LaboratoriesUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Ontario Research FundUNSPECIFIED
Swiss National Science Foundation (SNSF)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Army Research Office (ARO)W911NF-12-1-0521
University of SydneyUNSPECIFIED
Australian Research CouncilUNSPECIFIED
STW NetherlandsUNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Record Number:CaltechAUTHORS:20160622-170348845
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160622-170348845
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68616
Collection:CaltechAUTHORS
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 16:59
Last Modified:16 Aug 2017 23:46

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