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Title
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Quantum statistical manifolds : the finite-dimensional case
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Author
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Abstract
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| Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed. The emphasis is shifted from a manifold of strictly positive density matrices to a manifold M of faithful quantum states on a von Neumann algebra of bounded linear operators working on a Hilbert space. In order to avoid technicalities the theory is developed for the algebra of n-by-n matrices. A chart is introduced which is centered at a given faithful state omega(rho). It maps the manifold M onto a real Banach space of self-adjoint operators belonging to the commutant algebra. The operator labeling any state omega(rho) of M also determines a tangent vector in the point omega(rho). along the exponential geodesic in the direction of omega(sigma). A link with the theory of the modular automorphism group is worked out. Explicit expressions for the chart can be derived in terms of the modular conjugation and the relative modular operators. |
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Language
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English
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Source (journal)
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Lecture notes in computer science. - Berlin, 1973, currens
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Source (book)
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4th International SEE Conference on Geometric Science of Information, (GSI), AUG 27-29, 2019, ENAC, ENAC, Toulouse, FRANCE
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Publication
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Cham
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Springer international publishing ag
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2019
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ISBN
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978-3-030-26980-7
978-3-030-26979-1
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DOI
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10.1007/978-3-030-26980-7_65
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Volume/pages
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11712
(2019)
, p. 631-637
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ISI
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000535470100065
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Full text (Publisher's DOI)
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