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This paper establishes several converse bounds on the private transmission capabilities of a quantum channel.
Positive functions on C*-algebras
William F. Stinespring · 1955
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Conditional expectations in an operator algebra IV (entropy and information)
Hisaharu Umegaki · 1962
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E. B. Davies and J. T. Lewis · 1970
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Completely positive maps and entropy inequalities
Göran Lindblad · 1975
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The wire-tap channel
Aaron D. Wyner · 1975
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Quantum theory of open systems
Edward B. Davies · 1976
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The “transition probability” in the state space of a *-algebra
Armin Uhlmann · 1976
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Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
Armin Uhlmann · 1977
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Broadcast channels with confidential messages
Imre Csiszár and Janos Körner · 1978
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Quantum cryptography: Public key distribution and coin tossing
Charles H. Bennett and Gilles Brassard · 1984
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Quantum measuring processes of continuous observables
Masanao Ozawa · 1984
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Quasi-entropies for finite quantum systems
Dénes Petz · 1986
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Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Reinhard F. Werner · 1989
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The proper formula for relative entropy and its asymptotics in quantum probability
Fumio Hiai and Dénes Petz · 1991
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Common randomness in information theory and cryptography. I. Secret sharing
Rudolf Ahlswede and Imre Csiszár · 1993
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Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters · 1993
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Ueli M. Maurer · 1993
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Mixed-state entanglement and quantum error correction
Charles H. Bennett, David P. DiVincenzo, John A. Smolin, and William K. Wootters · 1996
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Quantum data processing and error correction
Benjamin Schumacher and Michael A. Nielsen · 1996
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Teleportation of continuous quantum variables
Samuel L. Braunstein and H. J. Kimble · 1998
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Cryptographic distinguishability measures for quantum mechanical states
Christopher A. Fuchs and Jeroen van de Graaf · 1998
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Entanglement measures and purification procedures
Vlatko Vedral and Martin B. Plenio · 1998
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Quantum nonlocality without entanglement
Charles H. Bennett, David P. DiVincenzo, Christopher A. Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, and William K. Wootters · 1999
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Private quantum channels
Andris Ambainis, Michele Mosca, Alain Tapp, and Ronald de Wolf · 2000
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On quantum fidelities and channel capacities
Howard Barnum, Emanuel Knill, and Michael A. Nielsen · 2000
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Strong converse and Stein’s lemma in quantum hypothesis testing
Tomohiro Ogawa and Hiroshi Nagaoka · 2000
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Evaluating capacities of bosonic Gaussian channels
Alexander S. Holevo and Reinhard F. Werner · 2001
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All teleportation and dense coding schemes
Reinhard F. Werner · 2001
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Remarks on the classical capacity of quantum channel
Alexander S. Holevo · 2002
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Relative error of state-dependent cloning
Alexey E. Rastegin · 2002
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Robustness of quantum gates in the presence of noise
Aram W. Harrow and Michael A. Nielsen · 2003
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Entanglement breaking channels
Michal Horodecki, Peter W. Shor, and Mary Beth Ruskai · 2003
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A lower bound on the relative error of mixed-state cloning and related operations
Alexey E. Rastegin · 2003
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“Squashed entanglement”: An additive entanglement measure
Matthias Christandl and Andreas Winter · 2004
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Quantum privacy and quantum wiretap channels
Ning Cai, Andreas Winter, and Raymond W. Yeung · 2004
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The private classical capacity and quantum capacity of a quantum channel
Igor Devetak · 2005
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Distance measures to compare real and ideal quantum processes
Alexei Gilchrist, Nathan K. Langford, and Michael A. Nielsen · 2005
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Secure key from bound entanglement
Karol Horodecki, Michał Horodecki, Paweł Horodecki, and Jonathan Oppenheim · 2005
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Strong converse theorems in quantum information theory
Hiroshi Nagaoka · 2005
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The Structure of Bipartite Quantum States: Insights from Group Theory and Cryptography
Matthias Christandl · 2006
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Multiplicativity of completely bounded p-norms implies a new additivity result
Igor Devetak, Marius Junge, Christopher King, and Mary Beth Ruskai · 2006
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Sine distance for quantum states
Alexey E. Rastegin · 2006
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Single-shot quantum state merging
Mario Berta · 2008
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Capacity of the bosonic wiretap channel and the entropy photon-number inequality
Saikat Guha, Jeffrey H. Shapiro, and Baris I. Erkmen · 2008
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Quantum key distribution based on private states: Unconditional security over untrusted channels with zero quantum capacity
Karol Horodecki, Michał Horodecki, Paweł Horodecki, Debbie Leung, and Jonathan Oppenheim · 2008
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Christian Weedbrook, Stefano Pirandola, Raul Garcia-Patron, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd · 2012
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One-shot classical-quantum capacity and hypothesis testing
Ligong Wang and Renato Renner · 2012
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Sandwiched Rényi divergence satisfies data processing inequality
Salman Beigi · 2013
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Monotonicity of a relative Rényi entropy
Rupert L. Frank and Elliott H. Lieb · 2013
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On quantum Rényi entropies: a new generalization and some properties
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Unconditional privacy over channels which cannot convey quantum information
Karol Horodecki, Michał Horodecki, Paweł Horodecki, Debbie Leung, and Jonathan Oppenheim · 2008
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Entanglement-breaking channels in infinite dimensions
Alexander S. Holevo · 2008
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Entanglement purification via separable superoperators
Eric M. Rains · 2008
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Private classical capacity with a symmetric side channel and its application to quantum cryptography
Graeme Smith · 2008
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Structured codes improve the Bennett-Brassard-84 quantum key rate
Graeme Smith, Joseph M. Renes, and John A. Smolin · 2008
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Quantum communication with zero-capacity channels
Graeme Smith and Jon Yard · 2008
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Postselection technique for quantum channels with applications to quantum cryptography
Matthias Christandl, Robert König, and Renato Renner · 2009
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Martin Müller-Lennert, Frédéric Dupuis, Oleg Szehr, Serge Fehr, and Marco Tomamichel · 2013
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Eric Chitambar, Debbie Leung, Laura Mančinska, Maris Ozols, and Andreas Winter · 2014
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Second-order coding rates for entanglement-assisted communication
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Ultimate classical communication rates of quantum optical channels
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Strong converse for a degraded wiretap channel via active hypothesis testing
Masahito Hayashi, Himanshu Tyagi, and Shun Watanabe · 2014
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Second order asymptotics for quantum hypothesis testing
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Strong converse exponent for classical-quantum channel coding
Milan Mosonyi and Tomohiro Ogawa · 2014
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“Pretty strong” converse for the quantum capacity of degradable channels
Ciara Morgan and Andreas Winter · 2014
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Cryptographic security of quantum key distribution
Christopher Portmann and Renato Renner · 2014
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Optimality of Gaussian discord
Stefano Pirandola, Gaetana Spedalieri, Samuel L. Braunstein, Nicolas J. Cerf, and Seth Lloyd · 2014
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A strong converse for the quantum state merging protocol
Naresh Sharma · 2014
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Fundamental rate-loss tradeoff for optical quantum key distribution
Masahiro Takeoka, Saikat Guha, and Mark M. Wilde · 2014
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The squashed entanglement of a quantum channel
Masahiro Takeoka, Saikat Guha, and Mark M. Wilde · 2014
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Mark M. Wilde, Andreas Winter, and Dong Yang · 2014
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Dawei Ding and Mark M. Wilde · 2015
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Superadditivity of private information for any number of uses of the channel
David Elkouss and Sergii Strelchuk · 2015
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On the power of ppt-preserving and non-signalling codes
Debbie Leung and William Matthews · 2015
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Quantum repeaters: Objectives, definitions and architectures
Norbert Lütkenhaus · 2015
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Information spectrum approach to strong converse theorems for degraded wiretap channels
Vincent Y. F. Tan and Matthieu R. Bloch · 2015
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Second-order asymptotics for the classical capacity of image-additive quantum channels
Marco Tomamichel and Vincent Y. F. Tan · 2015
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From Classical to Quantum Shannon Theory
Mark M. Wilde · 2015
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Decoding quantum information via the Petz recovery map
Salman Beigi, Nilanjana Datta, and Felix Leditzky · 2016
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