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The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy.
A Schwarz inequality for convex operator functions
C. Davis · 1957
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On general minimax theorems
M. Sion · 1958
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A fundamental property of quantum-mechanical entropy
E. H. Lieb and M. B. Ruskai · 1973
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Proof of the strong subadditivity of quantum-mechanical entropy
E. H. Lieb and M. B. Ruskai · 1973
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A Schwarz inequality for positive linear maps on C ∗ * -algebras
M. Choi · 1974
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Completely positive maps and entropy inequalities
G. Lindblad · 1975
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Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
A. Uhlmann · 1977
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Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
D. Petz · 1986
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Sufficiency of channels over von Neumann algebras
D. Petz · 1988
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A variational expression for the relative entropy
D. Petz · 1988
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The proper formula for relative entropy and its asymptotics in quantum probability
F. Hiai and D. Petz · 1991
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Distinguishability and accessible information in quantum theory
C. A. Fuchs · 1996
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The method of types [information theory]
I. Csiszár · 1998
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Asymptotics of quantum relative entropy from a representation theoretical viewpoint
M. Hayashi · 2001
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Optimal sequence of quantum measurements in the sense of Stein’s lemma in quantum hypothesis testing
M. Hayashi · 2002
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Jensen’s operator inequality
F. Hansen and G. K. Pedersen · 2003
Cited alongside, same era.
Monotonicity of quantum relative entropy revisited
D. Petz · 2003
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Quantum Information An Introduction
M. Hayashi · 2006
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Infinite Dimensional Analysis
C. D. Aliprantis and K. C. Border · 2007
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Positive Definite Matrices
On quantum Rényi entropies: A new generalization and some properties
M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel · 2013
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On variational expressions for quantum relative entropies, 2015
M. Berta, O. Fawzi, and M. Tomamichel · 2015
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Monotonicity of quantum relative entropy and recoverability
M. Berta, M. Lemm, and M. M. Wilde · 2015
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Quantum conditional mutual information, reconstructed states, and state redistribution
F. G. S. L. Brandão, A. W. Harrow, J. Oppenheim, and S. Strelchuk · 2015
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Quantum conditional mutual information and approximate Markov chains
O. Fawzi and R. Renner · 2015
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Universal recovery from a decrease of quantum relative entropy, 2015
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R. Bhatia · 2007
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Jensen’s operator inequality and its converses
F. Hansen, J. Pecaric, and I. Peric · 2007
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Quantum Information Theory and Quantum Statistics
D. Petz · 2008
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Trace Inequalities and Quantum Entropy: An Introductory Course
E. Carlen · 2009
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Relative entropy of entanglement and restricted measurements
M. Piani · 2009
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Quantum Systems, Channels, Information
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K. P. Seshadreesan and M. M. Wilde · 2015
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Recoverability in quantum information theory
M. M. Wilde · 2015
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The fidelity of recovery is multiplicative
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A. Müller-Hermes, D. Reeb, and M. M. Wolf · 2016
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