Study of universality in quantum entanglement and its application to quantum tomography and quantum control

• Project/Area Number: 21540413
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Atomic/Molecular/Quantum electronics
• Research Institution: Kanagawa University
• Principal Investigator: KUBOTANI Hiroto 神奈川大学, 工学部, 教授 (60281143)
• Co-Investigator(Kenkyū-buntansha): TODA Mikito 奈良女子大学, 理学部, 准教授 (70197896) ; ADACHI Satoshi 東京工業大学, 理工学研究科, 助教 (90211698)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 量子情報量子 / コンピュータ / ランダム行列理論 / 多変数超幾何関数 / 量子情報 / 量子コンピュータ / 量子絡み合い / ランダム行列

Research Abstract

We studied the universality of the statistics in the quantum entanglement generated by the dynamics of a bipartite system. The main points in our studies are two as follows. (1) We adopted the random matrices whose elements are all statistically random to model entangled quantum states. To this end, we developed theory of the random matrices in our original way. (2) We performed a large scale simulation of the quantum dynamics and obtained accurate one-body distribution of the Schmidt eigenvalues of entangled states generated by the quantum dynamics. We compared the one-body distribution with that derived in (1). This comparison revealed that the quantum chaotic dynamics shows the statistics of random matrices.

Research Products

• [Journal Article] Time series analysis of molecular dynamics simulation using wavelet (2012)
  • Author(s): M. Toda
  • Journal Title: 8th International Summer School/Conference LET's FACE CHAOS THROUGH NONLINEAR DYNAMICS Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] Time series analysis of molecular dynamics simulation using wavelet (2012)
  • Author(s): M.Toda
  • Journal Title: 8th International Summer School/Conference LET'S FACE CHAOS THROUGH NONLINEAR DYNAMICS Volume: (印刷中)(未定)
  • Peer Reviewed
• [Journal Article] Asymptotic analysis of singular values of rectangular complex matrices in the Laguerre and fixed-trace ensembles (2011)
  • Author(s): S. Adachi, M. Toda and H. Kubotani
  • Journal Title: Journal of Physics A : Math. Theor Volume: Vol.44 Pages: 292002-292002
  • Peer Reviewed
• [Journal Article] Dynamical Switching of a Reaction Coordinate to Carry the System through to a Different Product State at High Energies (2011)
  • Author(s): Hiroshi Teramoto, Mikito Toda
  • Journal Title: Physical Review Letters Volume: Vol.106
  • NAID: 120002834723
  • Peer Reviewed
• [Journal Article] Analysis of motion features for molecular dynamics simulation of proteins (2011)
  • Author(s): Mayumi Kamada, Mikito Toda, Masakazu Sekijima, Masami Takata, Kazuki Joe
  • Journal Title: Chemical Physics Letters Volume: Vol.502 Pages: 241-247
  • Peer Reviewed
• [Journal Article] Dynamical Switching of a Reaction Coordinate to Carry the System through to a Different ProductState at High Energies (2011)
  • Author(s): H. Teramoto, M. Toda and T. Komatsuzaki
  • Journal Title: Physical Reveiw Letters Volume: Vol.106 Pages: 54101-54101
  • Peer Reviewed
• [Journal Article] Analysis of motion features for molecular dynamics simulation of proteins (2011)
  • Author(s): M. Kamada, M. Toda, M. Sekijima, M. Takata, K. Joe
  • Journal Title: Chemical Phsysics Letters Volume: Vol.502 Pages: 241-247
  • Peer Reviewed
• [Journal Article] Stephen Berry, Ergodic Problems for Real Complex Systems in Chemical Physics (2011)
  • Author(s): Tamiki Komatsuzaki, Akinori Baba, Shinnosuke Kawai, Mikito Toda, John E. Straub, R
  • Journal Title: Advances in Chemical Physics Volume: Vol.145 Pages: 171-220
  • Peer Reviewed
• [Journal Article] Dynamical Reaction Theory based on Geometric Structures in Phase Space (2011)
  • Author(s): Shinnosuke Kawai, Hiroshi Teramoto, Chun-Biu Li, Tamiki Komatsuzaki, Mikito Toda
  • Journal Title: Advances in Chemical Physics Volume: Vol.145 Pages: 123-170
  • Peer Reviewed
• [Journal Article] Non-Brownian Phase Space Dynamics of Molecules, the Nature of their Vibrational States, and non-RRKM Kinetics (2011)
  • Author(s): David M. Leitner, Akira Shojiguchi, Mikito Toda, Yasuhiro Matsunaga, Chin-Biu Li, and Tamiki Komatsuzaki
  • Journal Title: Advances in Chemical Physics Volume: Vol.145 Pages: 83-122
  • Peer Reviewed
• [Journal Article] Asymptotic analysis of singular values of rectangular complex matrices in the Laguerre and fixed-trace ensembles (2011)
  • Author(s): S.Adachi, M.Toda, H.Kubotani
  • Journal Title: Journal of Physics A : Math.Theor. Volume: 44 Issue: 29 Pages: 292002-292002
  • DOI: 10.1088/1751-8113/44/29/292002
  • Peer Reviewed
• [Journal Article] Dynamical Switching of a Reaction Coordinate to Carry the System through to a Different Product State at High Energies (2011)
  • Author(s): H.Teramoto, M.Toda, T.Komatsuzaki
  • Journal Title: Physical Reveiw Letters Volume: 106 Issue: 5 Pages: 54101-54101
  • DOI: 10.1103/physrevlett.106.054101
  • NAID: 120002834723
  • Peer Reviewed
• [Journal Article] Analysis of motion features for molecular dynamics simulation of proteins (2011)
  • Author(s): M.Kamada, M.Toda, M.Sekijima, M.Takata, K.Joe
  • Journal Title: Chemical Phsysics Letters Volume: 502 Pages: 241-247
  • Peer Reviewed
• [Journal Article] Dynamical Switching of a Reaction Coordinate to Carry the System through to a Different Product State at High Energies (2011)
  • Author(s): Hiroshi Teramoto, Mikito Toda, Tamiki Komatsuzaki
  • Journal Title: Physical Review Letters Volume: Vol.106
  • NAID: 120002834723
  • Peer Reviewed
• [Journal Article] Clustering the Temporal Sequences Feature of 3D Protein Structure, Proceeding of the 2009 International Conference on Parallel and Distributed Processing Techniques and applications(PDPTA' 09) (2010)
  • Author(s): Mayumi Kamada, Sachi Kimura, Mikito Toda, Masami Takata, Kazuki Joe
  • Journal Title: Hamid R. Arabnia CSREA Press Pages: 749-755
  • Peer Reviewed
• [Journal Article] Ergodic Problems for Real Complex Systems in Chemical Physics (2010)
  • Author(s): Tamiki Komatsuzaki, Akinori Baba, Shinnosuke Kawai, Mikito Toda, John E.Straub, R.Stephen Berry
  • Journal Title: Advances in Chemical Physics 2 Pages: 749-755
  • Peer Reviewed
• [Journal Article] Dynamical Reaction Theory based on Geometric Structures in Phase Space (2010)
  • Author(s): Shinnosuke Kawai, Hiroshi Teramoto, Chun-Biu Li, Tamiki Komatsuzaki, Mikito Toda
  • Journal Title: Advances in Chemical Physics (未定(掲載決定))
  • Peer Reviewed
• [Journal Article] Non-Brownian Phase Space Dynamics of Molecules, the Nature of their Vibrational States, and non-RRKM Kinetics (2010)
  • Author(s): David M.Leitner, Akira Shojiguchi, Mikito Toda, Yasuhiro Matsunaga, Chin-Biu Li, Tamiki Komatsuzaki
  • Journal Title: Advances in Chemical Physics (未定(掲載決定))
  • Peer Reviewed
• [Journal Article] Clustering the Temporal Sequences Feature of 3D Protein Structure (2010)
  • Author(s): Mayumi Kamada, Sachi Kimura, Mikito Toda, Masami Takata, Kazuki Joe
  • Journal Title: Procceeding of the 2009 International Conference on Parallel and Distributed Processing Techniques and applications(PDPTA'09), (ed.Hamid R.Arabnia), (CSREA Press) (未定(出版予定))
  • Peer Reviewed
• [Journal Article] Random matrix theory of singular values of rectangular complex matrices I : Exact formula of one-body distribution function in fixed-trace ensemble (2009)
  • Author(s): S. Adachi, M. Toda and H. Kubotani
  • Journal Title: Annals of Physics Volume: Vol.324 Pages: 2278-2358
  • Peer Reviewed
• [Journal Article] Bifurcation of No-return Transition States in Many-body Chemical Reactions (2009)
  • Author(s): C-B Li, M. Toda and T. Komatsuzaki
  • Journal Title: Journal of Chemical Physics Volume: Vol.130 Pages: 124116-124122
  • Peer Reviewed
• [Journal Article] Dynamical Reaction Theory for Vibrationally Highly Excited Molecules, Progress in Ultrafast Intense Laser Physics IV (2009)
  • Author(s): Mikito Toda, K. Yamanouch, A. Becker, R. Li and S. L. Chin
  • Journal Title: Springer Pages: 91-112
  • Peer Reviewed
• [Journal Article] Overlooked Branch Cut in Steepest Descent Method-Switching Line and Atomic Domain (2009)
  • Author(s): T. Hyouguchi, R. Seto and S. Adachi
  • Journal Title: Progress of Theoretical Physics Volume: Vol.122 Pages: 1311-1346
  • NAID: 110007502692
  • Peer Reviewed
• [Journal Article] Overlooked Degree of Freedom in Steepest Descent Method-Steepest Descent Method Corresponding to Divergence-Free WKB Method- (2009)
  • Author(s): T. Hyouguchi, R. Seto and S. Adachi
  • Journal Title: Progress of Theoretical Physics Volume: Vol.122 Pages: 1347-1376
  • NAID: 110007502693
  • Peer Reviewed
• [Journal Article] Random matrix theory of singular values of rectangular complex matrices I : Exact formula of one-body distribution function in fixed-trace ensemble (2009)
  • Author(s): S.Adachi, M.Toda, H.Kubotani
  • Journal Title: Annals of Physics Vol.324 Pages: 2278-2358
  • Peer Reviewed
• [Journal Article] Bifurcation of No-return Transition States in Many-body Chemical Reactions (2009)
  • Author(s): C-B Li, M.Toda, T.Komatsuzaki
  • Journal Title: Journal of Chemical Physics Vol.130 Pages: 124116-124122
  • Peer Reviewed
• [Journal Article] Dynamical Reaction Theory for Vibrationally Highly Excited Molecules (2009)
  • Author(s): Mikito Toda
  • Journal Title: Progress in Ultrafast Intense Laser Physics IV, (ed.K.Yamanouchi, A.Becker, R.Li and S.L.Chin), (Springer) 4 Pages: 91-112
  • Peer Reviewed
• [Journal Article] Overlooked Branch Cut in Steepest Descent Method-Switching Line and Atomic Domain- (2009)
  • Author(s): T.Hyouguchi, R.Seto, S.Adachi
  • Journal Title: Progress of Theoretical Physics Vol.122 Pages: 1311-1346
  • NAID: 110007502692
  • Peer Reviewed
• [Journal Article] Overlooked Degree of Freedom in Steepest Descent Method-Steepest Descent Method Corresponding to Divergence-Free WKB Method- (2009)
  • Author(s): T.Hyouguchi, R.Seto, S.Adachi
  • Journal Title: Progress of Theoretical Physics Vol.122 Pages: 1347-1376
  • NAID: 110007502693
  • Peer Reviewed
• [Presentation] Universality in Dynamical Formation of Entanglement for Quantum Chaos (2009)
  • Author(s): Mikito Toda
  • Organizer: 12th Japan-Slovenia Seminar on Nonlinear Science
  • Place of Presentation: Hotel PIRAMIDA, Maribor, Slovenia.
  • Year and Date: 2009-10-07
• [Presentation] Universality in Dynamical Formation of Entanglement for Quantum Chaos (2009)
  • Author(s): Mikito Toda
  • Organizer: 12th Japan-Slovenia Seminar on Nonlinear Science
  • Place of Presentation: Maribor, Slovenia
  • Year and Date: 2009-10-07
• [Presentation] Fractional Behavior and Entanglement in Chaos (2009)
  • Author(s): Mikito Toda
  • Organizer: Nonlinear Dynamics in Quantum Systems
  • Place of Presentation: Siberian Federal University, Krasnoyarsk, Russia.
  • Year and Date: 2009-07-10
• [Presentation] Fractional Behavior and Entanglement in Chaos (2009)
  • Author(s): Mikito Toda
  • Organizer: Nonlinear Dynamics in Quantum Systems
  • Place of Presentation: Krasnoyarsk, Russia
  • Year and Date: 2009-07-10