The quantum information manifold for \(\varepsilon\)-bounded forms.

DOI10.1016/S0034-4877(00)90003-XzbMath1162.81387arXivmath-ph/9910031OpenAlexW1903598145MaRDI QIDQ5938510

R. F. Streater, M. R. Grasselli

Publication date: 22 July 2001

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

Full work available at URL: https://arxiv.org/abs/math-ph/9910031

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Geometry and quantization, symplectic methods (81S10) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

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 ⋮ The exponential Orlicz space in quantum information geometry ⋮ On the characterisation of paired monotone metrics ⋮ Quantum Orlicz Spaces in Information Geometry ⋮ Manifolds of classical probability distributions and quantum density operators in infinite dimensions ⋮ QUANTUM INFORMATION GEOMETRY AND NONCOMMUTATIVE L_p-SPACES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\alpha\)-divergence of the non-commutative information geometry
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Relative Hamiltonian for faithful normal states of a von Neumann algebra
• Differential-geometrical methods in statistics
• The Bogoliubov inner product in quantum statistics
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• Geometry of canonical correlation on the state space of a quantum system
• Geometries of quantum states