|
Title
|
|
|
|
Quantum statistical manifolds
| |
|
Author
|
|
|
|
| |
|
Abstract
|
|
|
|
| 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. |
| |
|
Language
|
|
|
|
English
| |
|
Source (journal)
|
|
|
|
Entropy: an international and interdisciplinary journal of entropy and information studies. - -
| |
|
Publication
|
|
|
|
2018
| |
|
ISSN
|
|
|
|
1099-4300
| |
|
DOI
|
|
|
|
10.3390/E20060472
| |
|
Volume/pages
|
|
|
|
20
:6
(2018)
, 17 p.
| |
|
Article Reference
|
|
|
|
472
| |
|
ISI
|
|
|
|
000436275400081
| |
|
Medium
|
|
|
|
E-only publicatie
| |
|
Full text (Publisher's DOI)
|
|
|
|
| |
|
Full text (open access)
|
|
|
|
| |
|