scholarly journals Quantum Statistical Manifolds

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 472 ◽  
Author(s):  
Jan Naudts
Keyword(s):  
Statistical Manifolds ◽  
Quantum Statistical

scholarly journals Dually flat structures induced from monotone metrics on a two-level quantum state space

2020 ◽  
Vol 135 (10) ◽  
Author(s):  
Akio Fujiwara
Keyword(s):  
State Space ◽  
Quantum State ◽  
Information Geometry ◽  
Central Importance ◽  
Flat Structure ◽  
Statistical Manifolds ◽  
Flat Structures ◽  
Quantum Statistical

AbstractThe notion of dually flatness is of central importance in information geometry. Nevertheless, little is known about dually flat structures on quantum statistical manifolds except that the Bogoliubov metric admits a global dually flat structure on a quantum state space $${{\mathcal {S}}}({{\mathbb {C}}}^d)$$ S ( C d ) for any $$d\ge 2$$ d ≥ 2 . In this paper, we show that every monotone metric on a two-level quantum state space $${{\mathcal {S}}}({{\mathbb {C}}}^2)$$ S ( C 2 ) admits a local dually flat structure.

scholarly journals Correction: Naudts, J. Quantum Statistical Manifolds. Entropy 2018, 20, 472

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 796
Author(s):  
Jan Naudts
Keyword(s):  
Statistical Manifolds ◽  
Quantum Statistical

Section 4 of “Naudts J. Quantum Statistical Manifolds. Entropy 2018, 20, 472” contains errors. They have limited consequences for the remainder of the paper. A new version of this Section is found here. Some smaller shortcomings of the paper are taken care of as well. In particular, the proof of Theorem 3 was not complete, and is therefore amended. Also, a few missing references are added.

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