Quantum conditional relative entropy and quasi-factorization of the relative entropy

DOI10.1088/1751-8121/aae4cfzbMath1414.81051arXiv1804.09525OpenAlexW3103110191WikidataQ59742192 ScholiaQ59742192MaRDI QIDQ4629597

Ángela Capel, Angelo Lucia, David Pérez-García

Publication date: 27 March 2019

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

Full work available at URL: https://arxiv.org/abs/1804.09525

zbMATH Keywords

mixing timelog-Sobolev inequalityconditional relative entropyquantum relative entropyPetz recovery mapquantum dissipative evolutionquasi-factorization of the relative entropy

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Measures of information, entropy (94A17) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57) Open systems, reduced dynamics, master equations, decoherence (81S22) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (9)

Quasi-factorization and multiplicative comparison of subalgebra-relative entropy ⋮ Shannon’s information theory 70 years on: applications in classical and quantum physics ⋮ Quantum reverse hypercontractivity: its tensorization and application to strong converses ⋮ A strengthened data processing inequality for the Belavkin–Staszewski relative entropy ⋮ Entropy decay for Davies semigroups of a one dimensional quantum lattice ⋮ Fisher information and logarithmic Sobolev inequality for matrix-valued functions ⋮ Approximate tensorization of the relative entropy for noncommuting conditional expectations ⋮ On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems ⋮ Stability of logarithmic Sobolev inequalities under a noncommutative change of measure

Cites Work

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• Swiveled Rényi entropies
• Quantum conditional mutual information and approximate Markov chains
• Multivariate trace inequalities
• Axiomatic characterizations of information measures
• Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
• Characterization of the relative entropy of states of matrix algebras
• Completely positive maps and entropy inequalities
• Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
• Approach to equilibrium of Glauber dynamics in the one phase region. II: The general case
• Squashed entanglement, \(\mathbf {k}\)-extendibility, quantum Markov chains, and recovery maps
• Entropy inequalities for unbounded spin systems
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Universal recovery maps and approximate sufficiency of quantum relative entropy
• Hypercontractivity and logarithmic Sobolev inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates
• Quantum reverse hypercontractivity: its tensorization and application to strong converses
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Quantum Gibbs samplers: the commuting case
• Relative entropy convergence for depolarizing channels
• Entropy production of doubly stochastic quantum channels
• CB-Norm Estimates for Maps Between NoncommutativeL_p-Spaces and Quantum Channel Theory
• Hypercontractivity of quasi-free quantum semigroups
• SUFFICIENCY OF CHANNELS OVER VON NEUMANN ALGEBRAS
• Efficient optimization of the quantum relative entropy
• Superadditivity of Quantum Relative Entropy for General States
• MONOTONICITY OF QUANTUM RELATIVE ENTROPY REVISITED
• α-z-Rényi relative entropies
• The $\chi ^2$χ2-divergence and mixing times of quantum Markov processes
• Quantum logarithmic Sobolev inequalities and rapid mixing
• On quantum Rényi entropies: A new generalization and some properties
• Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields

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