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Title
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Quantum statistical manifolds
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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 with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum states on the C*-algebra of bounded linear operators. In addition, ideas from the parameter-free approach to information geometry are adopted. The underlying Hilbert space is assumed to be finite-dimensional. In this way, technicalities are avoided so that strong results are obtained, which one can hope to prove later on in a more general context. Two different atlases are introduced, one in which it is straightforward to show that the quantum states form a Banach manifold, the other which is compatible with the inner product of Bogoliubov and which yields affine coordinates for the exponential connection. |
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Language
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English
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Source (journal)
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Entropy: an international and interdisciplinary journal of entropy and information studies. - -
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Publication
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2018
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ISSN
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1099-4300
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Volume/pages
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20
:6
(2018)
, 17 p.
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Article Reference
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472
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ISI
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000436275400081
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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