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Quantum relative entropies are jointly convex functions of two positive definite matrices that generalize the Kullback-Leibler divergence and arise naturally in quantum information theory.
Convex Analysis
R Tyrrell Rockafellar · 1970
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Convex trace functions and the Wigner-Yanase-Dyson conjecture
Elliott H. Lieb · 1973
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Proof of the strong subadditivity of quantum mechanical entropy
Elliott H. Lieb and Mary Beth Ruskai · 1973
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Concavity of certain maps on positive definite matrices and applications to Hadamard products
Tsuyoshi Ando · 1979
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C ∗ C^{*} -algebraic generalization of relative entropy and entropy
Viacheslav P Belavkin and P Staszewski · 1982
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Quasi-entropies for finite quantum systems
Dénes Petz · 1986
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Relative operator entropy in noncommutative information theory
JI Fujii · 1989
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov and Arkadii Nemirovskii · 1994
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Primal-dual interior-point methods for self-scaled cones
Yu E Nesterov and Michael J Todd · 1998
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Jensen’s operator inequality
Frank Hansen and Gert K Pedersen · 2003
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A matrix convexity approach to some celebrated quantum inequalities
Edward G. Effros · 2009
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Low-rank kernel learning with Bregman matrix divergences
Brian Kulis, Mátyás A Sustik, and Inderjit S Dhillon · 2009
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Matrix analysis: matrix monotone functions, matrix means, and majorization
Fumio Hiai · 2010
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Operator monotone functions, positive definite kernels and majorization
Mitsuru Uchiyama · 2010
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Numerical estimation of the relative entropy of entanglement
Yuriy Zinchenko, Shmuel Friedland, and Gilad Gour · 2010
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Perspectives of matrix convex functions
Ali Ebadian, Ismail Nikoufar, and Madjid Eshaghi Gordji · 2011
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Sandwiched Rényi divergence satisfies data processing inequality
Salman Beigi · 2013
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Matrix analysis
Rajendra Bhatia · 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
M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel · 2013
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The elements of integration and Lebesgue measure
Robert G Bartle · 2014
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Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy
M.M. Wilde, A. Winter, and D. Yang · 2014
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Mehdi Karimi and Levent Tunçel · 2019
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Self-concordance and matrix monotonicity with applications to quantum entanglement problems
Leonid Faybusovich and Cunlu Zhou · 2020
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Primal–dual interior-point methods for domain-driven formulations
Mehdi Karimi and Levent Tunçel · 2020
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Quantum Blahut-Arimoto algorithms
Navneeth Ramakrishnan, Raban Iten, Volkher Scholz, and Mario Berta · 2020
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From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
Haonan Zhang · 2020
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Geometric Rényi divergence and its applications in quantum channel capacities
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