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

2013 Fiscal Year Final Research Report

• Project/Area Number: 22740079
• 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: Shibaura 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
• Keywords: 量子力学の物理原理 / 一般確率論 / 相関

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.

Research Products

• [Journal Article] On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids (2014)
  • 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
  • Peer Reviewed
• [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
  • URL: http://ci.nii.ac.jp/naid/110009596571
  • Peer Reviewed
• [Journal Article] On the general property of correlation (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Distinguishability Measures and Entropies for General Probabilistic Theories (2010)
  • Author(s): Gen Kimura, Koji Nuida, Hideki Imai
  • Journal Title: Reports on Mathematical Physics Volume: 66 Pages: 175
  • DOI: 10.1016/S0034-4877(10)00025-X
  • Peer Reviewed
• [Journal Article] Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories (2010)
  • Author(s): Koji Nuida, Gen Kimura, Takayuki Miyadera
  • Journal Title: Journal of Mathematical Physics Volume: 51 Pages: 093505(30)
  • DOI: 10.1063/1.3479008
  • 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
• [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
• [Presentation] The power of Entanglement in General Probabilistic Theories - On the principle of Information Causality (2012)
  • 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
• [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
• [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
• [Presentation] On Basic Principles of General Probabilistic Theories (2011)
  • 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
• [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)