Random Matrix Theory and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800048
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: Collins Benoit 京都大学, 理学研究科, 准教授 (20721418)
• Co-Investigator(Renkei-kenkyūsha): Fukuda Motohisa 山形大学, 理学部, 准教授 (70771161) ; Matsumoto Sho 鹿児島大学, 理工学域理学系, 准教授 (60547553)
• Research Collaborator: Brannan Michael Texas A&M University, Department of Mathematics ; Zhong Ping University of Waterloo, Department of Mathematics ; Dahlqvist Antoine University of Cambridge, Statlab ; Kemp Todd University of California San Diego ; Nechita Ion CNRS ; Hyden Patrick Stanford University, Physics Department ; Gaudreau Lamarre Princeton University ; Pierre Yves Princeton University ; Kousha Termeh University of Ottawa, Departement of Mathematics and Statistics ; Kulik Rafal University of Ottawa, Departement of Mathematics and Statistics ; Szarek Tomasz University of Gdansk, Department of Mathematics ; Życzkowski Karol Jagiellonian University, Institute of Physics ; Szymański Konrad Jagiellonian University, Institute of Physics
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: Random matrices / quantum information

Outline of Final Research Achievements

In this research project, we investigated random matrices, which are matrices with random elements, via the moment method. Especially, we developed so-called Weingarten calculus and applied it to random matrix models which appear in quantum information theory.
For example, we gave a new approach to the problem of violation for the additivity of the minimum output entropy and obtained new examples in the problem of entanglement detection. These problems are quite
important problems in quantum information theory.

Free Research Field

functional analysis