Can Čencov meet Petz

DOI10.1007/978-3-031-38299-4_38arXiv2305.12482OpenAlexW4385434912MaRDI QIDQ6179026

L. González-Bravo, Fabio Di Cosmo, Florio M. Ciaglia

Publication date: 16 January 2024

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.12482

zbMATH Keywords

information geometry\(W^*\)-algebrasČencov's theoremPetz's theorem

Mathematics Subject Classification ID

Applications of selfadjoint operator algebras to physics (46L60)

Cites Work

• A characterization of W*-algebras
• Markov invariant geometry and manifolds of states
• Quasi-entropies for states of a von Neumann algebra
• Quasi-entropies for finite quantum systems
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Monotone metrics on matrix spaces
• Manifolds of classical probability distributions and quantum density operators in infinite dimensions
• Stratified manifold of quantum states, actions of the complex special linear group
• The General Form of γ-Family of Quantum Relative Entropies
• An Extended Cencov Characterization of the Information Metric
• Dynamical Vector Fields on the Manifold of Quantum States
• Information Geometry
• Geometry of quantum systems: density states and entanglement
• Strict positivity and D-majorization
• Information geometry, Jordan algebras, and a coadjoint orbit-like construction
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