Manifolds of classical probability distributions and quantum density operators in infinite dimensions

DOI10.1007/s41884-019-00022-1zbMath1444.46054arXiv1907.00732OpenAlexW3102626270MaRDI QIDQ2279964

Yanyan Li

Publication date: 17 December 2019

Published in: Information Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.00732

zbMATH Keywords

homogeneous spaces\(C^*\)-algebrasprobability distributionsquantum statesBanach manifolds

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Noncommutative dynamical systems (46L55) States of selfadjoint operator algebras (46L30) Infinite-dimensional manifolds (46T05)

Related Items

Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ Can Čencov meet Petz ⋮ On the pseudo-manifold of quantum states ⋮ Group actions and monotone metric tensors: the qubit case

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An infinite-dimensional statistical manifold modelled on Hilbert space
• Some considerations on topologies of infinite dimensional unitary coadjoint orbits
• A construction of a nonparametric quantum information manifold
• Geometric representation theory for unitary groups of operator algebras
• Derivations, dissipations and group actions on \(C^ *\)-algebras
• Infinite dimensional Lie transformation groups
• Linear algebraic groups in infinite dimensions
• Parametrized measure models
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces
• Information geometry and sufficient statistics
• Stratified manifold of quantum states, actions of the complex special linear group
• Unitary operators in \(C^ *\)-algebras
• Pure operations and measurements
• Symplectic leaves in real Banach Lie-Poisson spaces
• Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
• Riemannian geometry of finite rank positive operators
• Uniqueness of the Fisher–Rao metric on the space of smooth densities
• Normal pure states of the von Neumann algebra of bounded operators as Kahler manifold
• Symmetries, Group Actions, and Entanglement
• Quantum mechanics as an infinite-dimensional Hamiltonian system with uncertainty structure: Part I
• A note on dual Banach spaces.
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• Die Fisher-Information und symplektische Strukturen
• Geometry of quantum dynamics in infinite-dimensional Hilbert space
• Dynamical Vector Fields on the Manifold of Quantum States
• Quantum Orlicz Spaces in Information Geometry
• Duality versus dual flatness in quantum information geometry
• Wigner–Yanase information on quantum state space: The geometric approach
• Geometries of quantum states
• Information Geometry
• An Algebraic Approach to Quantum Field Theory
• On the integrability of quantum mechanics as an infinite dimensional Hamiltonian system
• Eléments de Mathématique. Groupes et algèbres de Lie
• Geometrization of quantum mechanics
• The quantum information manifold for \(\varepsilon\)-bounded forms.
• Theory of operator algebras I.

This page was built for publication: Manifolds of classical probability distributions and quantum density operators in infinite dimensions