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On correlation in general probabilistic theories and its application to quantum information theory

Research Project

Project/Area Number 22740079
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionShibaura Institute of Technology (2011-2013)
Chuo University (2010)

Principal Investigator

KIMURA Gen  芝浦工業大学, システム工学部, 助教 (80517011)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords量子力学の物理原理 / 一般確率論 / 相関 / 量子力学の原理 / 量子状態スペクトル / 量子情報理論 / (量子)相関 / 物理原理
Research Abstract

We studied a foundation of quantum mechanics and quantum information theory using the general probabilistic theories, which is considered to provide the most general framework of operationally valid probability theories. One of the goal of this study is to derive quantum mechanics based on purely physical principles, with the help of the recent development of the quantum information science. In particular, we have derived qubit system with appropriate physical principles and found general properties of correlations applicable to unconditionally secure key distribution.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (43 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (17 results) (of which Peer Reviewed: 11 results,  Open Access: 1 results) Presentation (25 results) (of which Invited: 5 results) Remarks (1 results)

  • [Journal Article] On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids2014

    • Author(s)
      Gen Kimura, Koji Nuida
    • Journal Title

      Journal of Geometry and Physics

      Volume: (掲載決定)

    • URL

      http://arxiv.org/abs/1012.5350

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Determining eigenvalues of a density matrix with minimal information in a single experimental setting2014

    • Author(s)
      T. Tanaka, Y. Ota, M. Kanazawa, G. Kimura, H. Nakazato, F. Nori
    • Journal Title

      Phys. Rev. A

      Volume: 89 Issue: 1

    • DOI

      10.1103/physreva.89.012117

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 量子力学の原理探究2013

    • Author(s)
      木村元
    • Journal Title

      科学基礎論研究

      Volume: 40 Pages: 23-28

    • NAID

      110009596571

    • URL

      http://ci.nii.ac.jp/naid/110009596571

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 情報から生まれる量子力学2013

    • Author(s)
      木村元
    • Journal Title

      日経サイエンス

      Volume: 7 Pages: 46-53

    • Related Report
      2013 Annual Research Report
  • [Journal Article] On determination of the purity of density operators with a minimal measurement model2013

    • Author(s)
      Gen Kimura
    • Journal Title

      International Workshop on Quantum Information Theory and Related Topics

      Volume: 1 Pages: 66-69

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Possibility of a minimal purity-measurement scheme critically depends on the parity of dimension of the quantum system2013

    • Author(s)
      Toru Tanaka, Gen Kimura and Hiromichi Nakazato
    • Journal Title

      Physical Review A

      Volume: 87 Issue: 1 Pages: 12303-12303

    • DOI

      10.1103/physreva.87.012303

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the general property of correlation2011

    • Author(s)
      Gen Kimura, Shuich Tasaki
    • Journal Title

      物性研究

      Volume: 97 Pages: 421-428

    • URL

      http://ci.nii.ac.jp/naid/110008799111

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mean King問題と量子誤り訂正符号2011

    • Author(s)
      吉田雅一, 宮寺隆之, 木村元, 今井秀樹
    • Journal Title

      第34回情報理論とその応用シンポジウム(電子ファイル)

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment2011

    • Author(s)
      C.Rodriguez-Rosario, G.Kimura, H.Imai, A.Guzik
    • Journal Title

      Physical Review Letters

      Volume: 106

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distinguishability Measures and Entropies for General Probabilistic Theories2011

    • Author(s)
      G.Kimura, K.Nuida, H.Imai
    • Journal Title

      Reports on Mathematical Physics

      Volume: (掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mean King Problemと量子誤り訂正符号2011

    • Author(s)
      吉田雅一, 宮寺隆之, 木村元, 今井秀樹
    • Journal Title

      2011年暗号と情報セキュリティシンポジウム(SCIS2011)予稿集

    • Related Report
      2010 Annual Research Report
  • [Journal Article] HBBプロトコルのInformation-Disturbance定理による安全性評価2011

    • Author(s)
      安藤元紀, 木村元, 宮寺隆之, 今井秀樹
    • Journal Title

      2011年暗号と情報セキュリティシンポジウム(SCIS2011)予稿集

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Distinguishability measures and entropies for general probabilistic theories2010

    • Author(s)
      Gen Kimura, Koji Nuida, Hideki Imai
    • Journal Title

      Reports on Mathematical Physics

      Volume: vol.66 Issue: 2 Pages: 175-206

    • DOI

      10.1016/s0034-4877(10)00025-x

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal observables for minimum-error state discrimination in general probabilistic theories2010

    • Author(s)
      Koji Nuida, Gen Kimura, Takayuki Miyadera
    • Journal Title

      Journal of Mathematical Physics

      Volume: vol.51 Issue: 9 Pages: 93505-93505

    • DOI

      10.1063/1.3479008

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 物理原理に基づく量子ビット系の導出2010

    • Author(s)
      木村元, 縫田光司, 今井秀樹
    • Journal Title

      第33回情報理論とその応用シンポジウム(SITA2010)予稿集

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Relation between the Dynamics of the Reduced Purity and Correlations2010

    • Author(s)
      G.Kimura, H.Ohno, M.Mosonyi
    • Journal Title

      Open System and Information Dynamics

      Volume: 17 Pages: 233-243

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories2010

    • Author(s)
      K.Nuida, G.Kimura, T.Miyadera
    • Journal Title

      Journal of Mathematical Physics

      Volume: 51

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 操作主義的確率論に基づく量子力学の原理探求2014

    • Author(s)
      木村元
    • Organizer
      量子論の諸問題と今後の発展
    • Place of Presentation
      高エネルギー加速器研究機構
    • Year and Date
      2014-03-10
    • Related Report
      2013 Final Research Report
  • [Presentation] 操作主義的確率論に基づく量子力学の原理探求2014

    • Author(s)
      木村元
    • Organizer
      量子論の諸問題と今後の発展
    • Place of Presentation
      高エネルギー加速器研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] CHSH演算子の最大期待値とその状態依存性2014

    • Author(s)
      鈴木亜弥子,木村元
    • Organizer
      量子論の諸問題と今後の発展
    • Place of Presentation
      高エネルギー加速器研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] 一般確率論上の情報理論及び量子力学の原理的理解について2013

    • Author(s)
      木村元
    • Organizer
      第29回量子情報技術研究会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2013-11-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 一般確率論上の情報理論及び量子力学の原理的理解について2013

    • Author(s)
      木村元
    • Organizer
      第29回量子情報技術研究会
    • Place of Presentation
      早稲田大学 理工学術院 西早稲田キャンパス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On determination of the purity of density operators with a minimal measurement model2013

    • Author(s)
      Gen Kimura
    • Organizer
      THE FIRST INTERNATIONAL WORKSHOP ON QUANTUM INFORMATION THEORY AND RELATED TOPICS
    • Place of Presentation
      DUY TAN UNIVERSITY
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 有限次元の測定系を用いた密度演算子の固有値測定2013

    • Author(s)
      田中 亨,金沢光矩,中里 弘道,木村 元
    • Organizer
      第29回量子情報技術研究会
    • Place of Presentation
      早稲田大学 理工学術院 西早稲田キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] The power of Entanglement in General Probabilistic Theories - On the principle of Information Causality2012

    • Author(s)
      Gen Kimura
    • Organizer
      ワークショップ「量子情報理論とその応用」
    • Place of Presentation
      立命館大学
    • Year and Date
      2012-12-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Mean King問題と量子誤り訂正符号2011

    • Author(s)
      吉田雅一
    • Organizer
      第34回情報理論とその応用シンポジウム
    • Place of Presentation
      ホテル森の風鶯宿
    • Year and Date
      2011-12-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] 量子力学の物理原理を求めて2011

    • Author(s)
      木村元
    • Organizer
      量子Student Chapter 13回
    • Place of Presentation
      国立情報学研究所(NII)(招待講演)
    • Year and Date
      2011-11-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] 量子力学の原理探求2011

    • Author(s)
      木村元
    • Organizer
      科学基礎論学会2011年度秋の研究例会 ---代数的観点からみた量子力学の基礎---
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2011-11-06
    • Related Report
      2013 Final Research Report
  • [Presentation] 量子力学の原理探究2011

    • Author(s)
      木村元
    • Organizer
      科学基礎論学会
    • Place of Presentation
      日本大学文理学部(招待講演)
    • Year and Date
      2011-11-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] 確率論から見る量子力学2011

    • Author(s)
      木村元
    • Organizer
      量子論の深化と発展
    • Place of Presentation
      東工大
    • Year and Date
      2011-09-13
    • Related Report
      2013 Final Research Report
  • [Presentation] On Basic Principles of General Probabilistic Theories2011

    • Author(s)
      Gen Kimura
    • Organizer
      Conceptual Foundations and Foils for Quantum Information Processing
    • Place of Presentation
      Perimeter Institute, Toronto, Canada
    • Year and Date
      2011-05-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Mean King Problemと量子誤り訂正符号2011

    • Author(s)
      吉田雅一, 宮寺隆之, 木村元, 今井秀樹
    • Organizer
      2011年暗号と情報セキュリティシンポジウム(SCIS2011)
    • Place of Presentation
      リーガロイヤルホテル小倉
    • Year and Date
      2011-01-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] HBBプロトコルのInformation-Disturbance定理による安全性評価2011

    • Author(s)
      安藤元紀, 木村元, 宮寺隆之, 今井秀樹
    • Organizer
      2011年暗号と情報セキュリティシンポジウム(SCIS2011)
    • Place of Presentation
      リーガロイヤルホテル小倉
    • Year and Date
      2011-01-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] 確率論から見る量子力学2011

    • Author(s)
      木村元
    • Organizer
      量子論の深化と発展
    • Place of Presentation
      東工大(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] On Basic Principles of General Probabilistic Theories2011

    • Author(s)
      Gen Kimura
    • Organizer
      Conceptual Foundations and Foils for Quantum Information Processing
    • Place of Presentation
      Perimeter Institute @ Toronto, Canada(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] 物理原理に基づく量子ビット系の導出2010

    • Author(s)
      木村元, 縫田光司, 今井秀樹
    • Organizer
      第33回情報理論とその応用シンポジウム(SITA2010)
    • Place of Presentation
      信州松代ロイヤルホテル
    • Year and Date
      2010-12-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] 反対称化演算子を用いた密度演算子の固有値測定

    • Author(s)
      田中 亨
    • Organizer
      日本物理学会 2013年春季大会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 反対称化演算子を用いた密度演算子の固有値測定

    • Author(s)
      田中 亨
    • Organizer
      第二回QUATUO研究会
    • Place of Presentation
      高知工科大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] The power of Entanglement in General Probabilistic Theories ―On the principle of Information Causality

    • Author(s)
      Gen Kimura
    • Organizer
      ワークショップ「量子情報理論とその応用」
    • Place of Presentation
      立命館大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Information Theory based on General Probabilistic Theories

    • Author(s)
      Gen Kimura
    • Organizer
      ワークショップ「量子情報理論とその応用」
    • Place of Presentation
      立命館大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 多体量子系における反対称化演算子を用いた密度演算子の固有値測定

    • Author(s)
      田中 亨
    • Organizer
      第27回量子情報技術研究会
    • Place of Presentation
      慶応大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 量子系の純粋度の最小構成測定方法と量子系の次元

    • Author(s)
      田中 亨
    • Organizer
      日本物理学会 2012年秋季大会
    • Place of Presentation
      横浜国立大
    • Related Report
      2012 Annual Research Report
  • [Remarks] 木村元, 情報から生まれる量子力学, 日経サイエンス, 7, 2013, 46-53 (本課題に関連する解説記事)

    • Related Report
      2013 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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