Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation

DOI10.1016/S0034-4877(97)81470-XzbMath1006.82502MaRDI QIDQ1373698

Hiroshi H. Hasegawa

Publication date: 13 March 2003

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

Mathematics Subject Classification ID

Parametric inference (62F99) Quantum equilibrium statistical mechanics (general) (82B10) Statistical aspects of information-theoretic topics (62B10)

Related Items (11)

INFORMATION GEOMETRY FOR SOME LIE ALGEBRAS ⋮ Monotone Riemannian metrics and dynamic structure factor in condensed matter physics ⋮ DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS ⋮ Quantum information criteria for model selection in quantum state estimation ⋮ Flat connections and Wigner-Yanase-Dyson metrics ⋮ Geometry of quantum states: Dual connections and divergence functions ⋮ Silver mean conjectures for 15-dimensional volumes and 14-dimensional hyperareas of the separable two-qubit systems ⋮ Bures geometry of three-level quantum systems ⋮ Continuity of the maximum-entropy inference ⋮ ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY ⋮ Qubit-qutrit separability-probability ratios

Cites Work

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• I-divergence geometry of probability distributions and minimization problems
• \(\alpha\)-divergence of the non-commutative information geometry
• Statistical dynamics
• Differential geometry of curved exponential families. Curvatures and information loss
• Differential-geometrical methods in statistics
• The Bogoliubov inner product in quantum statistics
• Geometry of canonical correlation on the state space of a quantum system
• Transport, Collective Motion, and Brownian Motion

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