Quantum approximate Markov chains are thermal

DOI10.1007/s00220-019-03485-6zbMath1482.81004arXiv1609.06636OpenAlexW3102283430WikidataQ127648529 ScholiaQ127648529MaRDI QIDQ2314432

Kohtaro Kato, Fernando G. S. L. Brandão

Publication date: 22 July 2019

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

Full work available at URL: https://arxiv.org/abs/1609.06636

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Quantum stochastic calculus (81S25) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (7)

Decay of quantum conditional mutual information for purely generated finitely correlated states ⋮ Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma ⋮ Matrix product states and the decay of quantum conditional mutual information ⋮ Entropy constraints for ground energy optimization ⋮ Finite correlation length implies efficient preparation of quantum thermal states ⋮ Locality at the boundary implies gap in the bulk for 2D PEPS ⋮ Classical restrictions of generic matrix product states are quasi-locally Gibbsian

Cites Work

• Quantum conditional mutual information and approximate Markov chains
• Robustness of quantum Markov chains
• Quantum graphical models and belief propagation
• Finite correlation length implies efficient preparation of quantum thermal states
• Exponential decay of correlations implies area law
• Gibbs states of a one dimensional quantum lattice
• Area Laws in Quantum Systems: Mutual Information and Correlations
• Information Theory and Statistical Mechanics
• Continuity of quantum conditional information
• The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
• Information topologies on non-commutative state spaces
• Expansional in banach algebras

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