Foundations of quantum theory from a universal viewpoint

2014 Fiscal Year Final Research Report

• Project/Area Number: 22740078
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University (2012-2014); National Institute of Advanced Industrial Science and Technology (2010-2011)
• Principal Investigator: MIYADERA Takayuki 京都大学, 工学(系)研究科(研究院), 准教授 (50339123)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 量子論基礎 / 量子測定 / 量子情報 / 一般確率論

Outline of Final Research Achievements

We studied the foundations of quantum theory from a universal point of view. Our findings include the followings: (1) some properties of quantum Kolmogorov complexity were obtained and its applicability to the quantum information was shown (2) the notion of quantum incompatibility was establihed (3) an order-theoretic structure behind the quantum incompatibility was revealed (4) state-discrimination problem in the convex approach was studied (5) the security of semiclassical quantum cryptography was examined (6) a limitation on the physical interaction in measurement processes was found.

Free Research Field

量子論基礎