Exploring Information Geometrical Methods in Noncommutative Probability Theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 22340019
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: Fujiwara Akio 大阪大学, 理学(系)研究科(研究院), 教授 (30251359)
• Co-Investigator(Kenkyū-buntansha): NAGAOKA Hiroshi 電気通信大学, 情報システム学研究科, 教授 (80192235)
• Co-Investigator(Renkei-kenkyūsha): OHARA Atsumi 福井大学, 工学研究科, 教授 (90221168) ; MABUCHI Toshiki 大阪大学, 理学研究科, 名誉教授 (80116102)
• Project Period (FY): 2010-04-01 – 2016-03-31
• Keywords: 情報幾何学 / 量子確率空間 / 量子統計学

Outline of Final Research Achievements

Aiming at establishing quantum information geometrical methods in noncommutative statistics, we studied the following: 1) Information geometry of renormalization groups, 2) Information geometry of quantum nuisance parameters, 3) Finslerian information geometry, 4) Flattenability of quantum monotone metrics, 5) Experimental verification of adaptive quantum state estimation theory, 6) Quantum local asymptotic normality, 7) Chentsov's theorem revisited, 8) Information geometrical structure induced from sandwiched quantum Renyi relative entropy.

Free Research Field

数物系科学