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Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies.
F. Kraus: Über konvexe matrixfunktionen ; Math. Z. 41
1936
Earlier work this paper cites.
A. Rényi: On measures of entropy and information ; Proc. 4th Berkeley Symp. on Math. Statist. Probability 1
1961
Earlier work this paper cites.
S.M. Ali, S.D. Silvey: A general class of coefficients of divergence of one distribution from another ; J. Roy. Stat. Soc. Ser. B, 28
1966
Earlier work this paper cites.
I. Csiszár: Information type measure of difference of probability distributions and indirect observations ; Studia Sci. Math. Hungar. 2
1967
Earlier work this paper cites.
M. Takesaki: Conditional expectations in von Neumann algebras ; J. Funct. Anal. 9
1972
Earlier work this paper cites.
I. Ekeland, R. Temam: Convex Analysis and Variational Problems ; North-Holland, American Elsevier (1976)
1976
Earlier work this paper cites.
A. Uhlmann: The “transition probability” in the state space of a ∗ -algebra ; Rep. Math. Phys. 9
1976
Earlier work this paper cites.
M. Mosonyi: Entropy, Information and Structure of Composite Quantum States ; PhD thesis, Catholic University of Leuven, 2005; https://repository.cc.kuleuven.be/dspace/ handle/1979/41
1979
Earlier work this paper cites.
F. Hansen and G.K. Pedersen: Jensen’s inequality for operators and Löwner’s theorem ; Math. Ann. 258
1982
Earlier work this paper cites.
D. Petz: Quasi-entropies for states of a von Neumann algebra ; Publ. RIMS. Kyoto Univ. 21
1985
Earlier work this paper cites.
J. Tomiyama: On the geometry of positive maps in matrix algebras. II ; Linear Algebra and Its Applications 69
1985
Earlier work this paper cites.
D. Petz: Quasi-entropies for finite quantum systems ; Rep. Math. Phys. 23
1986
Earlier work this paper cites.
F. Liese, I. Vajda: Convex Statistical Distances ; B.G. Teubner Verlagsgesellschaft, Leipzig, (1987)
1987
Earlier work this paper cites.
D. Petz: Sufficiency of channels over von Neumann algebras Quart. J. Math. Oxford Ser. (2) 39
1988
Earlier work this paper cites.
H. Araki: On an inequality of Lieb and Thirring ; Lett. Math. Phys. 19
1990
Earlier work this paper cites.
T. Cover, J.A. Thomas: Elements of Information Theory ; Wiley-Interscience, (1991)
1991
Earlier work this paper cites.
F. Hiai, D. Petz: The proper formula for relative entropy and its asymptotics in quantum probability ; Comm. Math. Phys. 143
1991
Cited alongside, same era.
I. Csiszár: Generalized cutoff rates and Rényi’s information measures ; IEEE Trans. Inf. Theory 41
1995
Cited alongside, same era.
R. Bhatia: Matrix Analysis ; Springer (1997)
1997
Cited alongside, same era.
A. Lesniewski, M.B. Ruskai: Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces ; J. Math. Phys. 40
1999
Cited alongside, same era.
T. Ogawa, H. Nagaoka: Strong converse and Stein’s lemma in quantum hypothesis testing ; IEEE Trans. Inform. Theory 47
2000
Cited alongside, same era.
M.B. Ruskai: Inequalities for Quantum Entropy: A Review with Conditions for Equality ; J. Math. Phys. 43
R. Bhatia: Positive Definite Matrices ; Princeton University Press (2007)
2007
Later among the works it cites.
M. Hayashi: Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding ; Phys. Rev. A 76
2007
Later among the works it cites.
F. Hiai, M. Mosonyi, T. Ogawa: Error exponents in hypothesis testing for correlated states on a spin chain ; J. Math. Phys. 49
2008
Later among the works it cites.
D. Petz: Quantum Information Theory and Quantum Statistics ; Springer (2008)
2008
Later among the works it cites.
E.G. Effros: A Matrix Convexity Approach to Some Celebrated Quantum Inequalities ; Proc. Natl. Acad. Sci. 106
2009
Later among the works it cites.
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2002
Cited alongside, same era.
D. Petz: Monotonicity of quantum relative entropy revisited ; Rev. Math. Physics. 15
2003
Cited alongside, same era.
P. Hayden, R. Jozsa, D. Petz, A. Winter: Structure of states which satisfy strong subadditivity of quantum entropy with equality ; Commun. Math. Phys. 246
2004
Cited alongside, same era.
M. Mosonyi, D. Petz: Structure of Sufficient Quantum Coarse Grainings ; Letters in Mathematical Physics 68
2004
Cited alongside, same era.
M. Ohya and D. Petz: Quantum entropy and its use ; Springer-Verlag, Heidelberg, (1993). Second edition (2004)
2004
Cited alongside, same era.
T. Ogawa: Perfect quantum error-correcting condition revisited ; arXiv:quant-ph/0505167, (2005)
2005
Cited alongside, same era.
M. Hayashi: Quantum Information: An Introduction ; Springer (2006)
2006
Cited alongside, same era.
2009
Later among the works it cites.
M. Nussbaum, A. Szkoła: A lower bound of Chernoff type for symmetric quantum hypothesis testing ; Ann. Statist. 37
2009
Later among the works it cites.
2009
Later among the works it cites.
M. Tomamichel, R. Colbeck, R. Renner: A Fully Quantum Asymptotic Equipartition Property ; IEEE Trans. Inf. Theory 55
2009
Later among the works it cites.
R. Blume-Kohout, H.K. Ng, D. Poulin, L. Viola: Information preserving structures: A general framework for quantum zero-error information ; Phys. Rev. A 82
2010
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F. Hiai: Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization (GSIS selected lectures); Interdisciplinary Information Sciences 16
2010
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A. Jenčová: Quantum hypothesis testing and sufficient subalgebras ; Lett. Math. Phys. 93
2010
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A. Jenčová, D. Petz, J. Pitrik: Markov triplets on CCR algebras ; Acta Sci. Math. (Szeged) 76
2010
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D. Petz: From f f -divergence to quantum quasi-entropies and their use ; Entropy 12
2010
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M. Mosonyi, F. Hiai: On the quantum Renyi relative entropies and related capacity formulas ; IEEE Trans. Inf. Theory, 57
2011
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