Quantum concentration inequalities
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Publication:2165074
DOI10.1007/s00023-022-01181-1zbMath1501.81002arXiv2106.15819OpenAlexW3173682849MaRDI QIDQ2165074
Cambyse Rouzé, Giacomo De Palma
Publication date: 18 August 2022
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2106.15819
Inequalities; stochastic orderings (60E15) Markov semigroups and applications to diffusion processes (47D07) Classical and relativistic thermodynamics (80A10) Statistical thermodynamics (82B30) Quantum state spaces, operational and probabilistic concepts (81P16) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)
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Cites Work
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- On the mean field and classical limits of quantum mechanics
- Quantum systems, channels, information. A mathematical introduction.
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Multivariate trace inequalities
- Ricci curvature of Markov chains on metric spaces
- On the relative entropy
- Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
- The proper formula for relative entropy and its asymptotics in quantum probability
- Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
- Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures
- On variational expressions for quantum relative entropies
- Finite correlation length implies efficient preparation of quantum thermal states
- Completely analytical interactions: Constructive description
- Structure of states which satisfy strong subadditivity of quantum entropy with equality
- Universal recovery maps and approximate sufficiency of quantum relative entropy
- From Poincaré inequalities to nonlinear matrix concentration
- Complete entropic inequalities for quantum Markov chains
- Gaussian concentration bound and ensemble equivalence in generic quantum many-body systems including long-range interactions
- Quantum optimal transport with quantum channels
- Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
- Noncommutative martingale deviation and Poincaré type inequalities with applications
- Stability of local quantum dissipative systems
- Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
- Concentration of measure without independence: a unified approach via the martingale method
- A new quantum version of \(f\)-divergence
- Quantum Gibbs samplers: the commuting case
- Concentration of Measure Inequalities in Information Theory, Communications, and Coding
- Connecting the probability distributions of different operators and generalization of the Chernoff–Hoeffding inequality
- A simple proof of the blowing-up lemma (Corresp.)
- Transport-Entropy Inequalities and Curvature in Discrete-Space Markov Chains
- Concentration of quantum states from quantum functional and transportation cost inequalities
- The Quantum Wasserstein Distance of Order 1
- Logarithmic Sobolev inequalities in discrete product spaces
- Quantum logarithmic Sobolev inequalities and rapid mixing
- An Introduction to Matrix Concentration Inequalities
- Quantum Information Processing with Finite Resources
- Prescribing a System of Random Variables by Conditional Distributions
- Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems
- Quantum Information Theory