Relative entropy convergence for depolarizing channels

DOI10.1063/1.4939560zbMath1332.81028arXiv1508.07021OpenAlexW2212795526MaRDI QIDQ2795547

Daniel Stilck França, Alexander Müller-Hermes, Michael M. Wolf

Publication date: 21 March 2016

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

Full work available at URL: https://arxiv.org/abs/1508.07021

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Measures of information, entropy (94A17) Channel models (including quantum) in information and communication theory (94A40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (11)

Quantum reverse hypercontractivity: its tensorization and application to strong converses ⋮ Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics ⋮ Trace distance ergodicity for quantum Markov semigroups ⋮ Geometric inequalities from phase space translations ⋮ Entropy decay for Davies semigroups of a one dimensional quantum lattice ⋮ Matrix Poincaré, Φ-Sobolev inequalities, and quantum ensembles ⋮ Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance ⋮ Concentration of quantum states from quantum functional and transportation cost inequalities ⋮ Quantum conditional relative entropy and quasi-factorization of the relative entropy ⋮ Entropy production of doubly stochastic quantum channels ⋮ Stability of logarithmic Sobolev inequalities under a noncommutative change of measure

Cites Work

• Modified logarithmic Sobolev inequalities in discrete settings
• Hypercontractivity in noncommutative \(L_1\) spaces
• Birkhoff's polytope and unistochastic matrices, \(N=3\) and \(N=4\)
• CB-Norm Estimates for Maps Between NoncommutativeL_p-Spaces and Quantum Channel Theory
• Modulus of convexity for operator convex functions
• Continuity bounds on the quantum relative entropy
• A Distribution Dependent Refinement of Pinsker's Inequality
• Entropy production for quantum dynamical semigroups
• Negative Entropy and Information in Quantum Mechanics
• Probability Inequalities for Sums of Bounded Random Variables
• Quantum logarithmic Sobolev inequalities and rapid mixing
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