Information theoretical representation and its applications of uncertainty principle in quantum theory

• Project/Area Number: 18740064
• 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: National Institute of Advanced Industrial Science and Technology
• Principal Investigator: MIYADERA Takayuki National Institute of Advanced Industrial Science and Technology, 情報セキュリティ研究センター, 研究員 (50339123)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,180,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥180,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥700,000 (Direct Cost: ¥700,000); Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
• Keywords: 量子論基礎 / 量子情報理論 / 量子測定 / 不確定性原理 / 量子コルモゴロフ複雑性 / 量子暗号 / 暗号・認証 / 情報基礎 / 暗号・認証等

Research Abstract

量子暗号に関する問題に動機付けられ、観測量の非可換性が情報理論にどのような制限を与えるか、についていくつかの視点から調べた。具体的には、(1)情報撹乱定理の一般化(2)トレース距離とフィデリティを用いた情報撹乱定理の導出(3)保存量があるときの測定過程の限界をあらわすWigner-Araki-Yanase 定理の量的表現の導出(4)Landau-Pollak 型不確定性関係の一般化(5)同時測定に関する不確定性原理の導出(6)量子コルモゴロフ複雑性を用いた量子暗号の安全性についての新しい定義と解析、を行った。

Research Products

• [Journal Article] Quantum Kolmogorov Complexity and Quantum Key Distribution (2009)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 79 Pages: 12324-12324
• [Journal Article] Quantum Kolmogorov complexity and quantum key distribution (2009)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Physical Review A 79
  • Peer Reviewed
• [Journal Article] Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures (with H. Imai) (2008)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 78 Pages: 52119-52119
• [Journal Article] Note on a universal quantum Turing machine (2008)
  • Author(s): S. Iriyama, T. Miyadera, M. Ohya
  • Journal Title: Phys. Lett. A 372 Pages: 5120-5120
• [Journal Article] Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures (2008)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Physical Review A 78
  • Peer Reviewed
• [Journal Article] Generalized Landau-Pollak Uncertainty Relation (with H. Imai) (2007)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 76 Pages: 62108-62108
• [Journal Article] Generalized Landau-Pollak Uncertainty Relation (2007)
  • Author(s): T.Miyadera, H.Imai
  • Journal Title: Physical Review A 76
  • Peer Reviewed
• [Journal Article] Strength of interaction for information distribution (2006)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 74 Pages: 64302-64302
• [Journal Article] Wigner-Araki-Yanase theorem on distinguishability (2006)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 74 Pages: 24101-24101
• [Journal Article] Information-Disturbance Theorem for Unbiased Observables (2006)
  • Author(s): T. Miyadera, H. Imai
  • Journal Title: Phys. Rev. A 73 Pages: 42317-42317
• [Journal Article] Information-Disturbance Theorem for Mutually Unbiased Observables (2006)
  • Author(s): T.Miyadera, H.Imai
  • Journal Title: Physical Review A 73 Pages: 42317-42317
• [Journal Article] Wigner-Araki-Yanase theorem on Distinguishability (2006)
  • Author(s): T.Miyadera, H.Imai
  • Journal Title: Physical Review A 74 Pages: 24101-24101
• [Journal Article] Strength of interaction for information distribution (2006)
  • Author(s): T.Miyadera, H.Imai
  • Journal Title: Physical Review A 74 Pages: 64302-64302
• [Presentation] 情報と撹乱-不確定性関係のさまざまな形- (2009)
  • Author(s): 宮寺 隆之
  • Organizer: 日本物理学会第64回年次大会
  • Place of Presentation: 立教大学 (シンポジウム依頼講演)
  • Year and Date: 2009-03-29
• [Presentation] Quantum Key Distribution and Quantum Algorithmic Information (2009)
  • Author(s): 宮寺 隆之、今井 秀樹
  • Organizer: SCIS2009
  • Place of Presentation: 大津
  • Year and Date: 2009-01-22
• [Presentation] Uncertainty Principle for Simultaneous Measurement of POVMs (2008)
  • Author(s): T. Miyadera
  • Organizer: Expository Quantum Lecture Series 2
  • Place of Presentation: Putra university
  • Year and Date: 2008-11-27
• [Presentation] Uncertainty Principle for Simultaneous Measurement of POVMs (2008)
  • Author(s): T. Miyadera
  • Organizer: Expository Quantum Lecture Series 2
  • Place of Presentation: Putra University, Malaysia
  • Year and Date: 2008-11-27
• [Presentation] Uncertainty relation between arbitrary POVM (2008)
  • Author(s): T. Miyadera
  • Organizer: GSIS workshop on quantum information theory
  • Place of Presentation: 東北大学 (依頼講演)
  • Year and Date: 2008-11-06
• [Presentation] State collapse in information transfer and its applications (2008)
  • Author(s): 宮寺 隆之、今井 秀樹
  • Organizer: SCIS2008
  • Place of Presentation: 宮崎
  • Year and Date: 2008-01-23
• [Presentation] Landau-Pollak 型不確定性関係の一般化 (2007)
  • Author(s): 宮寺 隆之、今井 秀樹
  • Organizer: SITA2007
  • Place of Presentation: 三重
  • Year and Date: 2007-11-28
• [Presentation] Information-Disturbance Theorem for General Observables (2007)
  • Author(s): 宮寺 隆之、今井 秀樹
  • Organizer: SCIS2007
  • Place of Presentation: 長崎
  • Year and Date: 2007-01-23
• [Presentation] 情報分配に必要な相互作用と一般化されたWigner-Araki-Yanase の定理 (2006)
  • Author(s): 宮寺 隆之、今井 秀樹
  • Organizer: SITA2006
  • Place of Presentation: 函館
  • Year and Date: 2006-12-01
• [Presentation] Uncertainty Principle and Oblivious Transfer (2006)
  • Author(s): T. Miyadera, H. Imai
  • Organizer: ISITA2006
  • Place of Presentation: ソウル
  • Year and Date: 2006-11-01