Mathematical study of quantum information

2013 Fiscal Year Final Research Report

• Project/Area Number: 21244007
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nagoya University
• Principal Investigator: OZAWA Masanao 名古屋大学, 情報科学研究科, 教授 (40126313)
• Co-Investigator(Kenkyū-buntansha): JIMBO Masakazu 名古屋大学, 大学院・情報科学研究科, 教授 (50103049) ; MATSUBARA Yo 名古屋大学, 大学院・情報科学研究科, 教授 (30242788) ; NISHIMURA Harumichi 名古屋大学, 大学院・情報科学研究科, 准教授 (70433323) ; HAMADA Mitsuru 玉川大学, 量子情報科学研究所, 教授 (10407679)
• Co-Investigator(Renkei-kenkyūsha): BUSCEMI Francesco 名古屋大学, 大学院・情報科学研究科, 准教授 (80570548)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Keywords: 数理物理学 / 量子測定 / 不確定性原理 / 量子情報 / 量子計算 / 量子符号 / 量子集合論 / 数学基礎論

Research Abstract

We developed new mathematical methods for quantum measurement theory, quantum set theory, quantum complexity theory, and quantum coding theory. We advanced the study of a universally valid reformulation of the uncertainty principle based on the Ozawa inequality. We experimentally observed the violation of Heisenberg's error-disturbance relation for the first time in the world and also confirmed the Ozawa inequality in the same experimental arrangement. We showed computational complexity, inevitable decoherence, and necessary physical resources for various models of quantum computation. Moreover, we developed a new coding to correcting those errors. Those results gave broad impacts on quantum information technology, related industries, and culture.

Research Products

• [Journal Article] Noise and Disturbance in QuantumMeasurements : An Information- Theoretic Approach (2014)
  • Author(s): F. Buscemi, M.J.W. Hall, M. Ozawa, M.M.Wilde
  • Journal Title: Physical Review Letters 112 Pages: 050401/1-050401/5
  • DOI: 10.1103/PhysRevLett.112.050401
  • Peer Reviewed
• [Journal Article] Experimental test of error-disturbance uncertainty relations by weak measurement (2014)
  • Author(s): F. Kaneda, S.-Y. Baek, M. Ozawa, K.Edamatsu
  • Journal Title: Physical Review Letters 112 Pages: 020402/1-020402/5
  • DOI: 10.1103/PhysRevLett.112.020402
  • Peer Reviewed
• [Journal Article] Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation (2013)
  • Author(s): S.-Y. Baek, F. Kaneda, M. Ozawa, K. Edamatsu
  • Journal Title: Scientific Reports 3 Pages: 2221/1-2221/5
  • DOI: 10.1038/srep02221
  • Peer Reviewed
• [Journal Article] General theory of envoronment-assisted entanglement distillation (2013)
  • Author(s): F. Buscemi, N. Datta
  • Journal Title: IEEE Transactions on Information Theory 59 Pages: 1940-1954
  • DOI: 10.1109/TIT.2012.2227673
  • Peer Reviewed
• [Journal Article] On Skinny Stationary Subsets of Pκλ (2013)
  • Author(s): Y. Matsubara, T. Usuba
  • Journal Title: Journal of Symbolic Logic 78 Pages: 667-680
  • DOI: 10.2178/jsl.7802180
  • Peer Reviewed
• [Journal Article] Quantum counterfeit coin problems (2013)
  • Author(s): K. Iwama, H. Nishimura, R. Raymond, J. Teruyama
  • Journal Title: Theoretical Computer Science 456 Pages: 329-352
  • DOI: 10.1016/j.tcs.2012.05.039
  • Peer Reviewed
• [Journal Article] All entangled states are nonlocal (2012)
  • Author(s): F. Buscemi
  • Journal Title: Physical Review Letters 108 Pages: 200401/1-200401/5
  • DOI: 10.1103/PhysRevLett.108.200401
  • Peer Reviewed
• [Journal Article] Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems (2012)
  • Author(s): S. P. Jordan, H. Kobayashi, D. Nagaj, H. Nishimura
  • Journal Title: Quantum Information & Computation 12 Pages: 461-471
  • Peer Reviewed
• [Journal Article] Comparison of quantum statistical models : equivalent conditions for sufficiency (2012)
  • Author(s): F. Buscemi
  • Journal Title: Communications in Mathematical Physics 310 Pages: 625-647
  • DOI: 10.1007/s00220-012-1421-3
  • Peer Reviewed
• [Journal Article] Experimental demonstration of auniversally valid error-disturbance uncertainty relation in spin measurements (2012)
  • Author(s): J. Erhart, S. Sponar, G. Sulyok, G. Badurek, M. Ozawa, Y. Hasegawa
  • Journal Title: Nature Physics 8 Pages: 185-189
  • DOI: 10.1038/NPHYS2194
  • Peer Reviewed
• [Presentation] Heisenberg's Uncertainty Relation : Violation and Reformulation, Emergent Quantum Mechanics (EmQM13) (2013)
  • Author(s): M. Ozawa
  • Organizer: 2nd International Symposium about Quantum Mechanics based on a Deeper Level Theory
  • Place of Presentation: Vienna, Austria
  • Year and Date: 2013-10-06
  • Invited
• [Presentation] Universally Valid Reformulation of Heisenberg's Uncertainty Principle (2013)
  • Author(s): M. Ozawa
  • Organizer: The 13th International Conference on Squeezed States and Uncertainty Relations(ICSSUR 2013)
  • Place of Presentation: Nuremberg, Germany
  • Year and Date: 2013-06-24
  • Invited
• [Presentation] Error-disturbance uncertainty relations in generalized photon polarization measurements (2013)
  • Author(s): K. Edamatsum, S.-Y. Beak, F. Kaneda, M. Ozawa
  • Organizer: 20th Central European Workshop on Quantum Optics
  • Place of Presentation: Stockholm, Sweden
  • Year and Date: 2013-06-20
  • Invited
• [Presentation] Universally valid Reformulation of the Heisenberg Uncertainty Principle (2013)
  • Author(s): M. Ozawa
  • Organizer: A Marcus Wallenberg Symposium "Quantum Theory : Advances and Problems"
  • Place of Presentation: Vaxjo, Sweden
  • Year and Date: 2013-06-12
  • Invited
• [Presentation] Quantum network coding ; How can network coding be applied to quantum information? (2013)
  • Author(s): H. Nishimura
  • Organizer: 2013 IEEE International Symposium on Network Coding (NetCod2013)
  • Place of Presentation: Calgary, Canada
  • Year and Date: 2013-06-09
  • Invited
• [Presentation] Overlooked restrictions on Euler angles in quantum computation (2013)
  • Author(s): M. Hamada
  • Organizer: American Physical Society March Meeting
  • Place of Presentation: Baltimore, USA
  • Year and Date: 2013-03-19
• [Presentation] Towards a one-shot entanglement theory (2013)
  • Author(s): F. Buscemi
  • Organizer: Workshop "Beyond i.i.d. in information theory"
  • Place of Presentation: Cambridge, England
  • Year and Date: 2013-01-09
  • Invited
• [Presentation] Simultaneous measurements and weak values (2011)
  • Author(s): M. Ozawa
  • Organizer: The Foundations of Probability and Physics-6 (FPP6)
  • Place of Presentation: Vaxjo, Sweden
  • Year and Date: 2011-06-13
  • Invited
• [Presentation] Universal uncertainty principle, simultaneous measurability, and weak values (2010)
  • Author(s): M. Ozawa
  • Organizer: The Tenth International Conference on Quantum Communication, Measurement and Computation (QCMC 2010)
  • Place of Presentation: Brisbane, Australia
  • Year and Date: 2010-07-19
• [Presentation] Quantum Reality and Measurement : Quantum Foundations Based on Quantum Logic and Set Theory, Quantum Theory : Reconsideration of Foundations (2009)
  • Author(s): M. Ozawa
  • Organizer: 5 (QTRF5)
  • Place of Presentation: Vaxjo, Sweden
  • Year and Date: 2009-06-15
  • Invited
• [Book] 数理物理 私の研究 (シュプリンガー量子数理シリーズ 第2巻), 量子測定理論 (2012)
  • Author(s): 南部洋一郎他共著 (荒木不二洋, 江口徹, 大矢雅則編), 分担:小澤正直
  • Total Pages: 119-125
  • Publisher: 丸善出版
• [Remarks] 2013年12月18日, 文部科学記者会見室, 『測定誤差と擾乱の不確定性に関する新 たな不等式の実験的検証に成功 』 (報道発表)
• [Remarks] 2013年7月17日, 文部科学記者会見室, 『ハイゼンベルクの測定誤差と擾乱に関 する不確定性関係の破れの実験的検証に 成功-光を用いた小澤の不等式の新たな検 証実験-』 (報道発表)
• [Remarks] 2012年1月13日, 文部科学記者会見室, 『現代物理学の根幹である不確定性原理 の破れを観測-ナノの世界の深淵を語る基本原理に穴-』 (報道発表)
• [Remarks] 2014年1月1日発行, 科学新聞(朝刊) ; 12月25日発行, 中日(朝刊) ; 日経(夕刊) (新聞等掲載)
• [Remarks] 2013年8月8日発行, 朝日(朝刊) ; 7月18日発行, 読売(朝刊) ; 日経(朝刊) ; 中日(朝刊) ; 日刊工業(朝刊) ; 河北新報(朝刊) (新聞等掲載)
• [Remarks] 2013年11月1日発行, Physics World [online] News (新聞等掲載)
• [Remarks] 2013年6月27日発行, Nature 498, 419-420, News (新聞等掲載)
• [Remarks] 2013年6月4日発行, 中日(朝刊) ; 5月31日 発行, 中日(朝刊) ; 5月3日発行, 中日(朝刊) (新聞等掲載)
• [Remarks] 2012年10月20日発行, Science News Vol. 182, No. 8, p. 15 (新聞等掲載)
• [Remarks] 2012年9月7日発行, 科学新聞 (新聞等掲載)
• [Remarks] 2012年8月31日発行, 朝日(朝刊) (新聞等掲載)
• [Remarks] 2012年6月1日発行, 『日経サイエンス』 (pp. 16～17) (新聞等掲載)
• [Remarks] 2012年4月28日発行, 朝日(夕刊) (新聞等掲載)
• [Remarks] 2012年4月1日発行, 『日経サイエンス』 (pp.34～43) (新聞等掲載)
• [Remarks] 2012年3月11日発行, 日経(朝刊) (新聞等掲載)
• [Remarks] 2012年2月28日発行, 毎日(朝刊) (新聞等掲載)
• [Remarks] 2012年2月9日発行, 日経(夕刊) (新聞等掲載)
• [Remarks] 2012年2月1日発行, 中日(朝刊) (新聞等掲載)
• [Remarks] 2012年1月30日発行, アエラ (p. 31) (新聞等掲載)
• [Remarks] 2012年1月27日発行, 朝日(朝刊) ; 1月23日 発行, 朝日(朝刊) ; 日刊工業(朝刊) ; 1月22 日発行, 読売(朝刊) (新聞等掲載)
• [Remarks] 2012年1月20日発行, Physics World [online] News (新聞等掲載)
• [Remarks] 2012年1月18日発行, 中日(夕刊) (新聞等掲載)
• [Remarks] 2012年1月16日発行, 朝日(朝刊) ; 日経(朝刊) ; 毎日(朝刊) ; 読売(朝刊) ; 中日(朝刊) 他 (新聞等掲載)
• [Remarks]
  • URL: http://www.math.cm.is.nagoya-u.ac.jp/~ozawa/
• [Remarks]
  • URL: http://researchmap.jp/ozawa/