Hypercontractivity and the logarithmic Sobolev inequality for the completely bounded norm

DOI10.1063/1.4934729zbMath1337.47056arXiv1509.02610OpenAlexW3106207327MaRDI QIDQ2786611

Salman Beigi, Christopher K. King

Publication date: 15 February 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02610

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Operator spaces and completely bounded maps (46L07) Quantum measurement theory, state operations, state preparations (81P15) Equations and inequalities involving linear operators, with vector unknowns (47A50) Algebraic systems of matrices (15A30) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items

Quantum Fourier analysis, Quantum reverse hypercontractivity: its tensorization and application to strong converses, Operator-valued Schatten spaces and quantum entropies, Contractivity properties of a quantum diffusion semigroup, Exponential decay of matrix Φ-entropies on Markov semigroups with applications to dynamical evolutions of quantum ensembles, Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles, Fisher information and logarithmic Sobolev inequality for matrix-valued functions, Concentration of quantum states from quantum functional and transportation cost inequalities, Hypercontractivity and logarithmic Sobolev inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates, Stability of logarithmic Sobolev inequalities under a noncommutative change of measure

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