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We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time.
Some inequalities satisfied by the quantities of information of fisher and shannon
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Vittorio Gorini, Andrzej Kossakowski, and Ennackal Chandy George Sudarshan · 1976
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Goran Lindblad · 1976
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Fred B Weissler · 1980
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Mihai Pimsner and Sorin Popa · 1986
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Tensor products of operator spaces
David P Blecher and Vern I Paulsen · 1991
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Dénes Petz · 1991
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Nicholas Th Varopoulos, L Saloff-Coste, and Th Coulhon · 1991
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E Brian Davies and J Martin Lindsay · 1992
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Dominique Bakry · 1994
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Persi Diaconis and Laurent Saloff-Coste · 1996
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Gilles Pisier · 1998
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Edward G Effros and Zhong-Jin Ruan · 2000
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Generalization of an inequality by talagrand and links with the logarithmic sobolev inequality
Felix Otto and Cédric Villani · 2000
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The role of relative entropy in quantum information theory
Vlatko Vedral · 2002
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Alexander Müller-Hermes, Daniel Stilck França, and Michael M Wolf · 2016
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Ivan Bardet · 2017
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Gradient flow and entropy inequalities for quantum markov semigroups with detailed balance
Eric A Carlen and Jan Maas · 2017
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A brief history of the gkls equation
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Strong data processing inequalities for input constrained additive noise channels
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Geometric inequalities from phase space translations
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On contraction properties of markov kernels
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Theory of operator algebras II
Masamichi Takesaki et al · 2003
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Spectral gap, logarithmic sobolev constant, and geometric bounds
Michel Ledoux · 2004
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Mu-Fa Chen · 2005
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Hypoelliptic heat kernel inequalities on the heisenberg group
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Modified logarithmic sobolev inequalities in discrete settings
Sergey G Bobkov and Prasad Tetali · 2006
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Stefan Huber, Robert König, and Anna Vershynina · 2017
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Monotonicity of the quantum relative entropy under positive maps
Alexander Müller-Hermes and David Reeb · 2017
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Strong data-processing inequalities for channels and bayesian networks
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Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
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On contraction coefficients, partial orders and approximation of capacities for quantum channels
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Graph h \ \backslash ” ormander systems
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