Concepts of Probability in Quantum Mechanics

2019 Fiscal Year Final Research Report

• Project/Area Number: 15K01123
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Sociology/History of science and technology
• Research Institution: Nihon University
• Principal Investigator: KITAJIMA Yuichiro 日本大学, 生産工学部, 准教授 (40582466)
• Project Period (FY): 2015-04-01 – 2020-03-31
• Keywords: 科学哲学 / 確率 / 量子論 / 局所性 / 非文脈依存性

Outline of Final Research Achievements

Quantum theory is a probabilistic theory. It is impossible to predict a definite value of every observable, and only the probability distributions are given. The basic idea of hidden variable theories is to argue that probability arises because quantum states do not represent the ultimate information about the system, and that there are hidden variables by which values of all observables would be uniquely determined.
The necessity of a completion of quantum theory with additional hidden variables was advocated by Einstein. He used the locality condition in his argument. In my research, I formulated Einstein’s local operation in algebraic quantum field theory. Another result of hidden variables in quantum theory is Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. In this inequality, the noncontextuality condition is used instead of the locality condition. In this research, I showed that any normal state violates this inequality in the case of algebraic quantum field theory.

Free Research Field

科学哲学

Academic Significance and Societal Importance of the Research Achievements

量子力学が誕生し現在に至るまで，その概念的基礎に関して様々な議論がなされてきた。有名な例は，アインシュタイン・ポドルスキー・ローゼン（EPR）による議論である。この議論で使われていた量子的な性質は，現在量子情報の分野に応用されている。
こうした量子的な性質の概念的基礎を調べることによって，量子情報において何が行われているのか，さらには量子情報の背後にある世界観がどのようなものであるかを明らかにする一助となるであろう。