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Entropy, Vol. 20, Pages 472: Quantum Statistical Manifolds

Entropy, Vol. 20, Pages 472: Quantum Statistical Manifolds

Entropy doi: 10.3390/e20060472

Authors: Jan Naudts

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.

Authors:   Naudts, Jan
Journal:   Entropy
Volume:   20
edition:   6
Year:   2018
Pages:   472
DOI:   10.3390/e20060472
Publication date:   17-Jun-2018
Facts, background information, dossiers
  • quantum states
  • quantum
  • entropy
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