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Mathematical Research of Quantum Information and Quantum Computing

Research Project

Project/Area Number 14340028
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTohoku University

Principal Investigator

OZAWA Masanao  Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (40126313)

Co-Investigator(Kenkyū-buntansha) HIAI Fumio  Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (30092571)
OBATA Nobuaki  Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (10169360)
TAYA Hisao  Tohoku University, Graduate School of Information Sciences, Research Associate, 大学院・情報科学研究科, 助手 (40257241)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥11,400,000 (Direct Cost: ¥11,400,000)
Fiscal Year 2004: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2003: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2002: ¥4,000,000 (Direct Cost: ¥4,000,000)
Keywordsuncertainty principle / quantum measurement / quantum computing / quantum information / conservation law / completely positive maps / quantum gates / fault-tolerant quantum computing / 量子完全相関 / 量子回路 / 量子Turing機械 / 量子推定理論 / 量子Fisher情報量 / 測定誤差 / 擾乱 / Wigner-Araki-Yanaseの定理 / 制御否定ゲート
Research Abstract

1.Heisenberg's uncertainty principle, which gives the trade-off between measurement noise and disturbance, has been reconsidered. Its limitation of the validity has been clarified and the universally valid generalization (universal uncertainty principle) has been established. If any measuring apparatus measures an observable A with noise ε(A) and disturbance η(B) on B, we have the relation ε(A)η(B)+ε(A)σ(B)+σ(A)η(B)≧(1/2)|<[A,B]>|, where σ stands for the standard deviation in the state just before the measurement.
2.It has been shown that, if the noise ε(A) and the disturbance η(B) are statistically independent from the initial state of the measured object, we have the original Heisenberg relation ε(A)η(B)≧(1/2)|<[A,B]>|.
3.From the universal uncertainty principle, Wigner-Araki-Yanase (WAY), found in 1952 to set a limitation of measurements under conservation law, has been quantitatively generalized to a reciprocal relation between the mean-square-noise of the measurement and the variance of the conserved quantity.
4.As a consequence from the universal uncertainty principle, it has been shown that the angular momentum conservation law sets a limitation to the accuracy of quantum gate operations, the accuracy of the CNOT gate controlled by an interaction with n qubit ancilla system is limited with error probability at least 1/(4n^2), and the CNOT controlled by the electro-magnetic field with average photon N is limited with error probability at least 1/(16N).

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (120 results)

All 2005 2004 2003 2002 Other

All Journal Article (99 results) Book (1 results) Publications (20 results)

  • [Journal Article] Perfect correlations between noncommuting observables2005

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 335(1)

      Pages: 11-19

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Uniformity of quantum circuit families for error-free algorithms2005

    • Author(s)
      M.Ozawa, H.Nishimura
    • Journal Title

      Theoret.Comput.Sci. 332(1-3)

      Pages: 487-496

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Constraints for quantum logic arising from conservation laws and field fluctuations2005

    • Author(s)
      M.Ozawa, (J.Gea-Banacloche)
    • Journal Title

      J.Opt B : Quantum Semiclass.Opt. 7(発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free analog of pressure and its Legendre transform2005

    • Author(s)
      F.Hiai
    • Journal Title

      Comm.Math.Phys. (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A free logarithmic Sobolev inequality on the circle2005

    • Author(s)
      F.Hiai, D.Petz, Y.Ueda
    • Journal Title

      Canad.Math.Bull. (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] White noise operators associated with the Cochran--Kuo--Sengupta space2005

    • Author(s)
      N.Obata
    • Journal Title

      Proc.Japan--Germany Seminar (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit2005

    • Author(s)
      N.Obata, A.Hora
    • Journal Title

      Quantum Information V (World Scientific) (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Admissible white noise operators and their quantum white noise derivatives2005

    • Author(s)
      N.Obata, U.C.Ji
    • Journal Title

      Proc.of Infinite Dimensional Harmonic Analysis at Tubingen (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Asymptotic spectral analysis of growing graphs : Odd graphs and spidernets2005

    • Author(s)
      N.Obata, D.Igarashi
    • Journal Title

      Banach Center Publications (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Generalized white noise operators fields and quantum white noise derivatives2005

    • Author(s)
      N.Obata, A.Hora
    • Journal Title

      Rev.Sem.Congr.Soc.Math.France (発表予定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Perfect correlations between noncommuting observables2005

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 335

      Pages: 11-19

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uniformity of quantum circuit families for error-free algorithms2005

    • Author(s)
      M.Ozawa (with H.Nishimura)
    • Journal Title

      Theoret.Comput.Sci. 332

      Pages: 487-496

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uniformity of quantum circuit families for error-free algorithms2005

    • Author(s)
      H.Nishimura, M.Ozawa
    • Journal Title

      Theoret.Compt.Sci. 332(1-3)

      Pages: 487-496

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 不確定性原理・保存法則・量子計算2004

    • Author(s)
      小澤正直
    • Journal Title

      日本物理学会誌 59

      Pages: 157-165

    • NAID

      110002069559

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uncertainty relations for joint measurements of noncommuting observables2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 320

      Pages: 367-374

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum measurements, instruments, and uncertainty principle2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Interdis.Inf.Sci. 10

      Pages: 69-81

    • NAID

      110000071635

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uncertainty relations for noise and disturbance in generalized quantum2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Ann.Phys. 311(2)

      Pages: 350-416

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum estimation by local observables2004

    • Author(s)
      M.Ozawa, M.Hotta
    • Journal Title

      Phys.Rev.A 70(8)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Universal uncertainty principle and quantum state control under2004

    • Author(s)
      M.Ozawa
    • Journal Title

      AIP Conference Proceedings : Quantum Communication, Measurement and Computing 734

      Pages: 95-98

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 数理論理学と経験科学の接点2004

    • Author(s)
      小澤正直
    • Journal Title

      科学基礎論研究 32

      Pages: 9-17

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Submultiplicativity vs subadditivity for unitarily invariant norms2004

    • Author(s)
      F.Hiai, X.Zhan
    • Journal Title

      Linear Algebra Appl. 377

      Pages: 155-164

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free transportation cost inequalities via random matrix approximation2004

    • Author(s)
      F.Hiai, D.Petz, Y.Ueda
    • Journal Title

      Prob.Theory Related Fields 130

      Pages: 199-221

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum probabilistic approach to spectral analysis of star graphs2004

    • Author(s)
      N.Obata
    • Journal Title

      Interdiscip.Inform.Sci. 10

      Pages: 41-52

    • NAID

      110000071632

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Unitarity of Kuo's Fourier-Mehler transform2004

    • Author(s)
      N.Obata, U.C.Ji
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top 7

      Pages: 147-154

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space2004

    • Author(s)
      N.Obata, U.C.Ji
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 311-338

    • NAID

      10013122855

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Monotone independence, comb graphs and Bose--Einstein condensation2004

    • Author(s)
      N.Obata, L.Accardi, A.Ben Ghorbal
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top 7

      Pages: 419-435

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Heat equation associated with L'evy Laplacian2004

    • Author(s)
      N.Obata, H.Ouerdiane
    • Journal Title

      Proc.Int.Conf.Stochastic Analysis and Applications (Kluwer)

      Pages: 53-68

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum measurements, instruments, and uncertainty principle2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Interdisciplinary Inf.Sci. 10

      Pages: 69-81

    • NAID

      110000071635

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uncertainty relations for noise and disturbance in generalized quantum measurements2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Ann.Phys. 311

      Pages: 350-416

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum estimation by local observables2004

    • Author(s)
      M.Ozawa (with M.Hotta)
    • Journal Title

      Phys.Rev.A 70

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uncertainty principle, conservation lawas, and quantum computing2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Butsuri-Gakkai-Shi 59

      Pages: 157-165

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Empirical logic2004

    • Author(s)
      M.Ozawa
    • Journal Title

      J.Jpn.Ass.Phi.Sci. 32

      Pages: 9-17

    • NAID

      130001435440

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Submultiplicativity vs subadditivity for unitarily invariant norms2004

    • Author(s)
      F.Hiai (with X.Zhan)
    • Journal Title

      Linear Algebra Appl. 377

      Pages: 155-164

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free transportation cost inequalities via random matrix approximation2004

    • Author(s)
      F.Hiai (with D.Petz, Y.Ueda)
    • Journal Title

      Probab.Theory Related Fields 130

      Pages: 199-221

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Unitarity of Kuo's Fourier-Mehler transform2004

    • Author(s)
      N.Obata (with U.C.Ji)
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 7

      Pages: 147-154

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space2004

    • Author(s)
      N.Obata (with U.C.Ji)
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 311-338

    • NAID

      10013122855

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Monotone independence, comb graphs and Bose--Einstein condensation2004

    • Author(s)
      N.Obata (with L.Accardi, A.Ben Ghorbal)
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 7

      Pages: 419-435

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Universal uncertainty principle and quantum state control under conservation laws2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Proc.7th Int.Conf.on Quantum Communication, Measurement and Computing, AIP Conference Proceedings 734(edited by S.M.Barnett, E.Andersson, J.Jeffers, P.Ohberg, and O.Hirota)(American Institute of Physics, Melville)

      Pages: 95-98

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Heat equation associated with L'evy Laplacian2004

    • Author(s)
      N.Obata (with H.Ouerdiane)
    • Journal Title

      Proc.Int.Conf.Stochastic Analysis and Applications(edited by S.Albeverio, A.B.de Monvel and H.Ouerdiane)(Kluwer Academic Publishers)

      Pages: 53-68

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Uncertainty relations for noise and disturbance in generalized quantum measurements2004

    • Author(s)
      M.Ozawa
    • Journal Title

      Ann.Phys. 311(2)

      Pages: 350-416

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Quantum estimation by local observables2004

    • Author(s)
      M.Hotta, M.Ozawa
    • Journal Title

      Phys.Rev.A 70(8)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Universal uncertainty principle and quantum state control under conservation laws2004

    • Author(s)
      M.Ozawa
    • Journal Title

      AIP Conference Proceedings : Quantum Communication, Measurement and Comnuting 734

      Pages: 95-98

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Submultiplicativity vs subadditivity for unitarily invariant norms2004

    • Author(s)
      F.Hiai, X.Zhan
    • Journal Title

      Linear Algebra Appl 377

      Pages: 155-164

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Free transportation cost inequalities via random matrix approximation2004

    • Author(s)
      F.Hiai, D.Petz, Y.Ueda
    • Journal Title

      Probab.Theory Related Fields 130

      Pages: 199-221

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space2004

    • Author(s)
      U.C.Ji, N.Obata
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 311-338

    • NAID

      10013122855

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Monotone independence, comb graphs and Bose--Einstein condensation2004

    • Author(s)
      L.Accardi, A.Ben Ghorbal, N.Obata
    • Journal Title

      Infin.Dumen.Anal.Quantum Probab.Rel.Top 7

      Pages: 419-435

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Uncertainty principle for quantum instruments and computing2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Int.J.Quant.Inf. 1

      Pages: 569-588

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum state reduction and the repeatability hypothesis2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Ann.Japan Ass.Phil.Sci. 11

      Pages: 107-121

    • NAID

      110007033666

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Rev.A 67

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum Limits of Measurement and Computing Induced by Conservation Laws and Uncertainty Relations2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Proceedings of the 6^<th> International Conference on Quantum Communication, Measurement and Computing (Rinton Press, Princeton)

      Pages: 175-180

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Ozawa replies2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Rev.Lett. 91

      Pages: 89802-89802

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Physical content of Heisenberg's uncertainty relation : limitation and reformulation2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 318

      Pages: 21-29

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Automorphisms of free product-type and their crossed-products2003

    • Author(s)
      F.Hiai, Y.Ueda
    • Journal Title

      J.Operator Theory 50

      Pages: 119-130

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Central limit theorems for large graphs : Method of quantum decomposition2003

    • Author(s)
      Y.Hashimoto, A.Hora, N.Obata
    • Journal Title

      J.Math.Phys. 44

      Pages: 71-88

    • NAID

      120002337737

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A unified characterization theorem in white noise theory2003

    • Author(s)
      N.Obata, U.C.Ji
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 6

      Pages: 167-178

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] q-deformed Araki-Woods algebras2003

    • Author(s)
      F.Hiai
    • Journal Title

      Operator Algebras and Mathematical Physics (Theta, Bucharest) 6

      Pages: 169-202

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum decomposition and quantum central limit theorem2003

    • Author(s)
      N.Obata, A.Hora
    • Journal Title

      Fundamental Problems in Quantum Physics (World Scientific)

      Pages: 284-305

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum State Reduction and the Repeatability Hypothesis2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Ann.Japan Ass.Phil.Sci. 11

      Pages: 107-121

    • NAID

      110007033666

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Automorphisms of free product-type and their crossed-products2003

    • Author(s)
      F.Hiai (Y.Ueda)
    • Journal Title

      J.Operator Theory 50

      Pages: 119-130

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Central limit theorems for large graphs : Method of quantum decomposition2003

    • Author(s)
      N.Obata (with Y.Hashimoto, A.Hora)
    • Journal Title

      J.Math.Phys. 44

      Pages: 71-88

    • NAID

      120002337737

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A unified characterization theorem in white noise theory2003

    • Author(s)
      N.Obata (with Un Cig Ji)
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 6

      Pages: 167-178

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Means of Hilbert Space Operators2003

    • Author(s)
      F.Hiai (with H.Kosaki)
    • Journal Title

      Lecture Notes in Mathematics(Springer) 1820

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum limits of measurement and computing induced by conservation laws and uncertainty relations2003

    • Author(s)
      M.Ozawa
    • Journal Title

      Proc. 6th Int.Conf.on Quantum Communication, Measurement and Computing(edited by J.Shappiro and O.Hirota)(Rinton Press, Princeton)

      Pages: 175-180

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] q-deformed Araki-Woods algebras2003

    • Author(s)
      F.Hiai
    • Journal Title

      Operator Algebras and Mathematical Physics(edited by J.-M.Combes et al.)(Theta, Bucharest)

      Pages: 169-202

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum decomposition and quantum central limit theorem2003

    • Author(s)
      N.Obata (with A.Hora)
    • Journal Title

      Fundamental Problems in Quantum Physics(edited by L.Accardi and S.Tasaki)(World Scientific)

      Pages: 284-305

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Position Measuring Interactions and the Heisenberg Uncertainty Principle2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 299

      Pages: 1-7

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Halting of Quantum Turing Machines2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Proceedings of 3^<rd> International Conference on Unconventional Models of Computation (UMC2002) 276

      Pages: 58-65

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Conservative Quantum Computing2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Rev.Lett. 89

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inequalities involving unitarily invariant norms and operator monotone functions2002

    • Author(s)
      F.Hiai, X.Zhan
    • Journal Title

      Linear Algebra Appl. 341

      Pages: 151-169

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free relative entropy for measures and a corresponding perturbation theory2002

    • Author(s)
      F.Hiai, M.Mizuo, D.Petz
    • Journal Title

      J.Math.Soc.Japan 54

      Pages: 679-718

    • NAID

      10009480996

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum stochastic analysis via white noise operators in weighted Fock space2002

    • Author(s)
      N.Obata, D.M.Chung, U.C.Ji
    • Journal Title

      Rev.Math.Phys. 14

      Pages: 241-272

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Diagonalization of the Levy Laplacian and related stable processes2002

    • Author(s)
      N.Obata, H.-H.Kuo, K.Saito
    • Journal Title

      Infinite Dimen.Anal.Quantum Prob. 5

      Pages: 317-331

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition2002

    • Author(s)
      N.Obata, U.C.Ji, H.Ouerdiane
    • Journal Title

      Infinite Dimen.Anal.Quantum Prob. 5

      Pages: 395-407

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Computation of Iwasawa invariants2002

    • Author(s)
      H.Taya, T.Fukuda
    • Journal Title

      Transactions of Japan Society for Industrial and Applied Mathematics 12

      Pages: 293-306

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inverse S-transform, Wick product and overcompleteness of exponential vectors2002

    • Author(s)
      N.Obata
    • Journal Title

      Quantum Information IV (World Scientific)

      Pages: 147-176

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum white noise calculus, in Non-Commutativity2002

    • Author(s)
      N.Obata, U.C.Ji
    • Journal Title

      Infinite-Dimensionality and Probability at the Crossroads (World Scientific)

      Pages: 143-191

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Cauchy processes and the L'evy Laplacian, in Non-Commutativity2002

    • Author(s)
      N.Obata, K.Saito
    • Journal Title

      Infinite-Dimensionality and Probability at the Crossroads (World Scientific)

      Pages: 360-373

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Position measuring interactions and the Heisenberg uncertainty principle2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Lett.A 299

      Pages: 1-7

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Conservative quantum computing2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Phys.Rev.Lett 89

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inequalities involving unitarily invariant norms and operator monotone functions2002

    • Author(s)
      F.Hiai (with X.Zhan)
    • Journal Title

      Linear Algebra Appl. 341

      Pages: 151-169

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free relative entropy for measures and a corresponding perturbation theory2002

    • Author(s)
      F.Hiai (with M.Mizuo, D.Petz)
    • Journal Title

      J.Math.Soc.Japan 54

      Pages: 679-718

    • NAID

      10009480996

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum stochastic analysis via white noise operators in weighted Fock space2002

    • Author(s)
      N.Obata (with D.M.Chung, U.C.Ji)
    • Journal Title

      Rev.Math.Phys. 14

      Pages: 241-272

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Diagonalization of the Levy Laplacian and related stable processes2002

    • Author(s)
      N.Obata (with H.-H.Kuo, K.Saito)
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 5

      Pages: 317-331

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Analytic characterization of generalized Fock space operators as two-variable entire functions with growth condition2002

    • Author(s)
      N.Obata (with U.C.Ji, H.Ouerdiane)
    • Journal Title

      Infin.Dimen.Anal.Quantum Probab.Rel.Top. 5

      Pages: 395-407

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Computation of Iwasawa invariants2002

    • Author(s)
      H.Taya (with Takashi Fukuda)
    • Journal Title

      Transactions of Japan Society for Industrial and Applied Mathematics 12

      Pages: 293-306

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Halting of Quantum Turing Machines, in Unconventional Models of Computation2002

    • Author(s)
      M.Ozawa
    • Journal Title

      Lecture Notes in Computer Science 2509(edited by C.S.Calude, M.J.Dinneen, and F.Peper)(Springer, Berlin)

      Pages: 58-65

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Inverse S-transform, Wick product and overcompleteness of exponential vectors2002

    • Author(s)
      N.Obata
    • Journal Title

      Quantum Information IV(edited by T.Hida and K.Saito)(World Scientific)

      Pages: 147-176

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quantum white noise calculus2002

    • Author(s)
      N.Obata (with U.C.Ji)
    • Journal Title

      Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads(edited by N.Obata, T.Matsui and A.Hora)(World Scientific)

      Pages: 143-191

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Cauchy processes and the L'evy Laplacian2002

    • Author(s)
      N.Obata (with K.Saito)
    • Journal Title

      Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroads(edited by N.Obata, T.Matsui and A.Hora)(World Scientific)

      Pages: 360-373

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Constraints for quantum logic arising from conservation laws and field fluctuations

    • Author(s)
      M.Ozawa (with J.Gea-Banacloche)
    • Journal Title

      J.Opt.B : Quantum Semiclass. Opt.7(to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free analog of pressure and its Legendre transform

    • Author(s)
      F.Hiai
    • Journal Title

      Comm.Math.Phys. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A free logarithmic Sobolev inequality on the circle

    • Author(s)
      F.Hiai (with D.Petz, Y.Ueda)
    • Journal Title

      Canad.Math.Bull. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] White noise operators associated with the Cochran--Kuo--Sengupta space

    • Author(s)
      N.Obata
    • Journal Title

      Proc.Japan--Germany Seminar. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] An interacting Fock space with periodic Jacobi parameter obtained from regular graphs in large scale limit

    • Author(s)
      N.Obata (with A.Hora)
    • Journal Title

      Quantum Information V(edited by T.Hida and K.Saito)(World Scientific) (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Admissible white noise operators and their quantum white noise derivatives

    • Author(s)
      N.Obata (with U.C.Ji)
    • Journal Title

      Proc.of Infinite Dimensional Harmonic Analysis at Tubingen (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Asymptotic spectral analysis of growing graphs: Odd graphs and spidernets

    • Author(s)
      N.Obata (with D.Igarashi)
    • Journal Title

      Banach Center Publications (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Generalized white noise operators fields and quantum white noise derivatives

    • Author(s)
      N.Obata (with U.C.Ji)
    • Journal Title

      Rev.Sem.Congr.Soc.Math.France (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Free analog of pressure and its Legendre transform

    • Author(s)
      F.Hiai
    • Journal Title

      Comm.Math.Phys. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A free logarithmic Sobolev inequality on the circle

    • Author(s)
      F.Hiai, D.Petz, Y.Ueda
    • Journal Title

      Canad.Math.Bull. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Book] Means of Hilbert Space Operators (Lecture Notes in Mathematics, Vol.1820)2003

    • Author(s)
      F.Hiai, H.Kosaki
    • Total Pages
      148
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum state reduction and the repeatability hypothesis"Ann.Japan Ass.Phil.Sci.. 11. 107-121 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement"Phys.Rev.A. 67. 042105-1-042105-6 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masanao Ozawa: "Quantum Limits of Measurement and Computing Induced by Conservation Laws and Uncertainty Relations"Proceedings of the 6^<th> International; Conference on Quantum Communication, Measurement and Computing (Rinton Press, Princeton). 175-180 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Ozawa replies"Phys.Rev.Lett.. 91. 089802 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Physical content of Heisenberg's uncertainty relation : limitation and reformulation"Phys.Lett.A. 318. 21-29 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Uncertainty principle for quantum instruments and computing"International Journal of Quantum Information. 1. 569-588 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Uncertainty relations for joint measurements of noncommuting observables"Phys.Lett.A. 320. 367-374 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Ozawa: "Uncertainty relations for noise and disturbance in generalized quantum measurements"Ann.Phys.(N.Y.). (印刷中).

    • Related Report
      2003 Annual Research Report
  • [Publications] Masanao Ozawa: "Quantum measurements, instruments, and uncertainty principle"Interdisciplinary Information Sciences. 10. 69-81 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 小澤正直: "不確定性原理・保存法則・量子計算"日本物理学会誌. 59. 157-165 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] F.Hirai, Y.Ueda: "Automorphisms of free product-type and their crossed-products"J.Operator Theory. 50. 119-130 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] F.Hiai, X.Zhan: "Submultiplicativity vs subadditivity for unitarily invariant norms"Linear Algebra Appl.. 377. 155-164 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Hashimoto, A.Hora, N.Obata: "Central limit theorems for large graphs : Method of quantum decomposition"J.Math.Phys.. 44. 71-88 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] U.C.Ji, N.Obata: "A unified characterization theorem in white noise theory"Infin.Dimen.Anal.Quantum Probab.Rel.Top.. 6. 167-178 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masanao Ozawa: "Position Measuring Interactions and the Heisenberg Uncertainty Principle"Physics Letters A. 299. 1-7 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Harumichi Nishimura, Masanao Ozawa: "Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines"Theoretical Computer Science A. 276. 147-181 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masanao Ozawa: "Conservative Quantum Computing"Physical Review Letters. 89. 057902(1)-057902(4) (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masanao Ozawa: "Halting of Quantum Turing Machines"Proceedings of 3^<rd> International Conference on Unconventional Models of Computation (UMC2002). 58-65 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masanao Ozawa: "Universally Valid Reformulation of the Heisenberg Uncertainty Principle on Noise and Disturbance in Measurement"Physical Review A. (発表予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masanao Ozawa: "Quantum Limits of Measurement and Computing Induced by Conservation Laws and Uncertainty Relations"Proceedings of the 6^<th> International Conference on Quantum Communication, Measurement and Computing (QCMC'02). (発表予定). (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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