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Concepts of Probability in Quantum Mechanics

Research Project

Project/Area Number 15K01123
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Sociology/History of science and technology
Research InstitutionNihon 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
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords科学哲学 / 確率 / 量子論 / 局所性 / 非文脈依存性 / 量子力学 / 完全性 / アインシュタイン / 局所性原理 / 文脈依存性 / 隠れた変数 / ライヘンバッハ / 共通原因
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.

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。

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (10 results)

All 2020 2019 2018 2017 2015

All Journal Article (7 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 1 results,  Acknowledgement Compliant: 2 results) Presentation (3 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] 情報の観点からみた量子力学2020

    • Author(s)
      北島雄一郎
    • Journal Title

      現代思想

      Volume: 48(2) Pages: 73-83

    • Related Report
      2019 Annual Research Report
  • [Journal Article] 量子力学の完全性をめぐって-EPR論文とアインシュタインによる論文の相違点-2019

    • Author(s)
      北島雄一郎
    • Journal Title

      現代思想

      Volume: 47(10) Pages: 77-90

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory2018

    • Author(s)
      Yuichiro Kitajima
    • Journal Title

      Nagoya Winter Workshop: Reality and Measurement in Algebraic Quantum Theory

      Volume: 261 Pages: 83-95

    • DOI

      10.1007/978-981-13-2487-1_3

    • ISBN
      9789811324864, 9789811324871
    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Contextuality in Algebraic Quantum Theory2018

    • Author(s)
      北島雄一郎
    • Journal Title

      Journal of the Japan Association for Philosophy of Science

      Volume: 45 Issue: 1-2 Pages: 23-34

    • DOI

      10.4288/kisoron.45.1-2_23

    • NAID

      130006732289

    • ISSN
      0022-7668, 1884-1236
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A state-dependent noncontextuality inequality in algebraic quantum theory2017

    • Author(s)
      Yuichiro Kitajima
    • Journal Title

      Physics Letters A

      Volume: 381 Issue: 29 Pages: 2305-2312

    • DOI

      10.1016/j.physleta.2017.05.033

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] `Reichenbachian common cause systems of size 3 in general probability theories2017

    • Author(s)
      Yuichiro Kitajima
    • Journal Title

      Making it Formally Explicit (edited by G. Hofer-Szabo et al.), European Studies in Philosophy of Science 6

      Volume: - Pages: 129-145

    • DOI

      10.1007/978-3-319-55486-0_7

    • ISBN
      9783319554853, 9783319554860
    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Characterizing common cause closedness of quantum probability theories2015

    • Author(s)
      Yuichiro Kitajima and Miklos Redei
    • Journal Title

      Studies in History and Philosophy of Modern Physics

      Volume: 52 Pages: 234-241

    • DOI

      10.1016/j.shpsb.2015.08.003

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] 論理的観点からみた量子力学2018

    • Author(s)
      北島雄一郎
    • Organizer
      日本科学哲学会
    • Related Report
      2018 Research-status Report
  • [Presentation] 量子力学における文脈依存性2017

    • Author(s)
      北島雄一郎
    • Organizer
      日本科学哲学会
    • Related Report
      2017 Research-status Report
  • [Presentation] Common cause closedness in orthomodular lattices2015

    • Author(s)
      Yuichiro Kitajima
    • Organizer
      15th CONGRESS OF LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
    • Place of Presentation
      Helsinki (Finland)
    • Year and Date
      2015-08-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2021-02-19  

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