Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups
Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension...
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| Veröffentlicht in: | Annales Henri Poincaré 2023, Vol.24 (3), p.717-750 |
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| container_title | Annales Henri Poincaré |
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| creator | Wirth, Melchior Zhang, Haonan |
| description | Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups. |
| doi_str_mv | 10.1007/s00023-022-01220-x |
| format | Article |
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| ispartof | Annales Henri Poincaré, 2023, Vol.24 (3), p.717-750 |
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| source | SpringerNature Journals |
| subjects | Algebra Classical and Quantum Gravitation Concavity Curvature Dynamical Systems and Ergodic Theory Elementary Particles Group theory Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Matrices (mathematics) Multipliers Original Paper Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Semigroups Theoretical |
| title | Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups |
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