Complete entropic inequalities for quantum Markov chains
From MaRDI portal
Publication:2149079
DOI10.1007/s00205-022-01785-1zbMath1501.46053arXiv2102.04146OpenAlexW3167394113MaRDI QIDQ2149079
Publication date: 28 June 2022
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.04146
Noncommutative probability and statistics (46L53) Channel models (including quantum) in information and communication theory (94A40) Quantum entropies (81P17) Quantum channels, fidelity (81P47)
Related Items
Quasi-factorization and multiplicative comparison of subalgebra-relative entropy ⋮ Quantum concentration inequalities ⋮ Optimal convergence rate in the quantum Zeno effect for open quantum systems in infinite dimensions ⋮ Derivations and KMS-symmetric quantum Markov semigroups ⋮ Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics ⋮ Entropy decay for Davies semigroups of a one dimensional quantum lattice ⋮ Stability of logarithmic Sobolev inequalities under a noncommutative change of measure
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local random quantum circuits are approximate polynomial-designs
- Monotonicity of the quantum relative entropy under positive maps
- Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
- Modified logarithmic Sobolev inequalities in discrete settings
- The subelliptic heat kernel on \(\mathbf{SU}(2)\): representations, asymptotics and gradient bounds
- Long-time asymptotic properties of dynamical semigroups on W*-algebras
- The proper formula for relative entropy and its asymptotics in quantum probability
- The equivalence of the logarithmic Sobolev inequality and the Dobrushin- Shlosman mixing condition
- Non-commutative symmetric Markov semigroups
- Completely positive maps and entropy inequalities
- On the generators of quantum dynamical semigroups
- Spreading of sets in product spaces and hypercontraction of the Markov operator
- Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
- Hypercontractivity and logarithmic Sobolev inequalities for the Clifford- Dirichlet form
- Hypercontractivity in noncommutative \(L_1\) spaces
- Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras
- On contraction properties of Markov kernels
- Exponential decay of entropy in the random transposition and Bernoulli-Laplace models
- On certain properties of the relative entropy of states of operator algebras
- Entropy inequalities for unbounded spin systems
- Monotone metrics on matrix spaces
- Universal recovery maps and approximate sufficiency of quantum relative entropy
- Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
- Approximate tensorization of the relative entropy for noncommuting conditional expectations
- Quantum reverse hypercontractivity: its tensorization and application to strong converses
- Fisher information and logarithmic Sobolev inequality for matrix-valued functions
- Complete gradient estimates of quantum Markov semigroups
- The free Markoff field
- Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
- Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
- Strong data-processing inequalities for channels and Bayesian networks
- Quantum Gibbs samplers: the commuting case
- Strong converse and Stein's lemma in quantum hypothesis testing
- Contraction coefficients for noisy quantum channels
- Entropy production of doubly stochastic quantum channels
- Strong Data Processing Inequalities and <inline-formula> <tex-math notation="LaTeX">$\Phi $ </tex-math> </inline-formula>-Sobolev Inequalities for Discrete Channels
- Quantum Communication with Zero-Capacity Channels
- Mixed-norm inequalities and operator space 𝐿_{𝑝} embedding theory
- Expander graphs and their applications
- On Divergences and Informations in Statistics and Information Theory
- Modified log-sobolev inequalities, mixing and hypercontractivity
- Entropy and index for subfactors
- Hypothesis testing and information theory
- Monotone Riemannian metrics and relative entropy on noncommutative probability spaces
- Concentration of quantum states from quantum functional and transportation cost inequalities
- Min- and Max-Relative Entropies and a New Entanglement Monotone
- Group Transference Techniques for the Estimation of the Decoherence Times and Capacities of Quantum Markov Semigroups
- The detectability lemma and quantum gap amplification
- The $\chi ^2$χ2-divergence and mixing times of quantum Markov processes
- Quantum logarithmic Sobolev inequalities and rapid mixing
- Logarithmic Sobolev inequalities in non-commutative algebras
- Conditional expectation in an operator algebra. IV. Entropy and information
- Inner Product Modules Over B ∗ -Algebras
- On Information and Sufficiency
- Relative entropy for von Neumann subalgebras
- Recovery map stability for the data processing inequality
- Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields
