ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY

DOI10.1142/S0219025701000462zbMath1039.81011arXivmath-ph/0006030OpenAlexW2963085863MaRDI QIDQ4460443

R. F. Streater, M. R. Grasselli

Publication date: 18 May 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0006030

zbMATH Keywords

monotone metricsBogoliubov-Kubo-Mori metricinvertible density matrices

Mathematics Subject Classification ID

Quantum computation (81P68) Applications of global differential geometry to the sciences (53C80) Quantum measurement theory, state operations, state preparations (81P15) Information theory (general) (94A15) Statistical aspects of information-theoretic topics (62B10)

Related Items (16)

Geometric algebra and information geometry for quantum computational software ⋮ Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS ⋮ Duality versus dual flatness in quantum information geometry ⋮ A geometry on the space of probabilities. II: Projective spaces and exponential families ⋮ Entropy and geometry of quantum states ⋮ Reconstructing the relaxation dynamics induced by an unknown heat bath ⋮ A generalized quantum relative entropy ⋮ G-dual teleparallel connections in information geometry ⋮ Flat connections and Wigner-Yanase-Dyson metrics ⋮ On the characterisation of paired monotone metrics ⋮ Silver mean conjectures for 15-dimensional volumes and 14-dimensional hyperareas of the separable two-qubit systems ⋮ From quasi-entropy to various quantum information quantities ⋮ The General Form of γ-Family of Quantum Relative Entropies ⋮ Proof of a Modified Jaynes's Estimation Theory ⋮ Qubit-qutrit separability-probability ratios

Cites Work

• Quasi-entropies for finite quantum systems
• \(\alpha\)-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
• On the Riemannian metric of \(\alpha\)-entropies of density matrices
• CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE L^p-SPACES
• Geometry of canonical correlation on the state space of a quantum system
• Geometries of quantum states
• Transport, Collective Motion, and Brownian Motion

This page was built for publication: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY