https://doi.org/10.1140/epjp/s13360-020-00877-9
Regular Article
Dually flat structures induced from monotone metrics on a two-level quantum state space
Department of Mathematics, Osaka University, 560-0043, Toyonaka, Osaka, Japan
a
fujiwara@math.sci.osaka-u.ac.jp
Received:
24
June
2020
Accepted:
22
October
2020
Published online:
27
October
2020
The 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 
for any 
. In this paper, we show that every monotone metric on a two-level quantum state space 
admits a local dually flat structure.
© The Author(s) 2020
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
