Geometry of quantum states: Dual connections and divergence functions

DOI10.1016/S0034-4877(01)90008-4zbMath0984.81022WikidataQ128114448 ScholiaQ128114448MaRDI QIDQ5933512

Anna Jenčová

Publication date: 23 August 2001

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

torsiongeodesicsmonotone metricquantum state spaceRiemannian curvaturetorsion-free affine connections

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99)

Related Items (12)

A construction of a nonparametric quantum information manifold ⋮ Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS ⋮ G-dual teleparallel connections in information geometry ⋮ Topologies on quantum states ⋮ Flat connections and Wigner-Yanase-Dyson metrics ⋮ On the monotonicity of scalar curvature in classical and quantum information geometry ⋮ On the characterisation of paired monotone metrics ⋮ Alpha-beta log-determinant divergences between positive definite trace class operators ⋮ Continuity of the maximum-entropy inference ⋮ QUANTUM INFORMATION GEOMETRY AND NONCOMMUTATIVE L_p-SPACES ⋮ The General Form of γ-Family of Quantum Relative Entropies

Cites Work

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• \(\alpha\)-divergence of the non-commutative information geometry
• Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation
• Monotone metrics on matrix spaces
• Differential-geometrical methods in statistics
• Geometries of quantum states

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