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Correction published on 17 October 2018, see Entropy 2018, 20(10), 796.
Article

Quantum Statistical Manifolds

Departement Fysica, Universiteit Antwerpen, Universiteitsplein 1, 2610 Wilrijk Antwerpen, Belgium
Entropy 2018, 20(6), 472; https://doi.org/10.3390/e20060472
Received: 26 May 2018 / Revised: 15 June 2018 / Accepted: 15 June 2018 / Published: 17 June 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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. View Full-Text
Keywords: quantum states; exponential connection; parameter-free information geometry; Banach manifold; GNS-representation quantum states; exponential connection; parameter-free information geometry; Banach manifold; GNS-representation
MDPI and ACS Style

Naudts, J. Quantum Statistical Manifolds. Entropy 2018, 20, 472. https://doi.org/10.3390/e20060472

AMA Style

Naudts J. Quantum Statistical Manifolds. Entropy. 2018; 20(6):472. https://doi.org/10.3390/e20060472

Chicago/Turabian Style

Naudts, Jan. 2018. "Quantum Statistical Manifolds" Entropy 20, no. 6: 472. https://doi.org/10.3390/e20060472

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