A construction of a nonparametric quantum information manifold

DOI10.1016/j.jfa.2006.02.007zbMath1111.46038arXivmath-ph/0511065OpenAlexW2138794130MaRDI QIDQ852603

Anna Jenčová

Publication date: 15 November 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0511065

zbMATH Keywords

relative entropydual connectionsinformation manifoldquantum Orlicz spacestate perturbation

Mathematics Subject Classification ID

Quantum computation (81P68) General theory of von Neumann algebras (46L10) Applications of selfadjoint operator algebras to physics (46L60) Quantum stochastic calculus (81S25) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Noncommutative function spaces (46L52) Information theory (general) (94A15) States of selfadjoint operator algebras (46L30) Infinite-dimensional manifolds (46T05)

Related Items (max. 100)

Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ Monotone norms and Finsler structures in noncommutative spaces ⋮ Information geometry, Jordan algebras, and a coadjoint orbit-like construction ⋮ Parametric models and information geometry on \(W^\star\)-algebras ⋮ The exponential Orlicz space in quantum information geometry ⋮ A statistical manifold modeled on Orlicz spaces using Kaniadakis \(\kappa\)-exponential models ⋮ Manifolds of classical probability distributions and quantum density operators in infinite dimensions

Cites Work

• Dual connections in nonparametric classical information geometry
• Defining the curvature of a statistical problem (with applications to second order efficiency)
• The exponential statistical manifold: mean parameters, orthogonality and space transformations
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Differential-geometrical methods in statistics
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• Quantum Orlicz Spaces in Information Geometry
• Noncommutative Orlicz spaces associated to a state
• QUANTUM INFORMATION GEOMETRY AND NONCOMMUTATIVE L_p-SPACES
• An invariant form for the prior probability in estimation problems
• Geometry of quantum states: Dual connections and divergence functions
• The quantum information manifold for \(\varepsilon\)-bounded forms.
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