Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

DOI10.1016/j.physleta.2010.10.005zbMath1238.81013arXiv1009.5219OpenAlexW2037905966WikidataQ29030800 ScholiaQ29030800MaRDI QIDQ418637

Paolo Facchi, Ravi Kulkarni, E. C. G. Sudarshan, Vladimir I. Man'ko, Franco Ventriglia, Giuseppe Marmo

Publication date: 29 May 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5219

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Quantum state spaces, operational and probabilistic concepts (81P16) Quantum state estimation, approximate cloning (81P50)

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Cites Work

• Unnamed Item
• Entanglement and decoherence. Foundations and modern trends. Lectures given at the international summer school on ``Quantum information, Dresden, Germany, September 2005
• On the meaning and interpretation of tomography in abstract Hilbert spaces
• Maximum Fisher information in mixed state quantum systems
• Remarks on the GNS Representation and the Geometry of Quantum States
• Geometrization of statistical mechanics
• Statistical distance and the geometry of quantum states
• Fisher information in quantum statistics
• On Quantum Statistical Inference
• Wigner–Yanase information on quantum state space: The geometric approach
• Uniqueness of the Haag-Ruelle Scattering States

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