1998 Fiscal Year Annual Research Report

情報力学の研究とその数理的応用

Research Project

Project/Area Number	09044100
Research Institution	SCIENCE UNIVERSITY OF TOKYO
Principal Investigator	大矢雅則東京理科大学, 理工学部, 教授 (90112896)
Co-Investigator(Kenkyū-buntansha)	FREUDENBERG ダブリューフランデンベルグ技術大学, 数学科, 教授井上啓東京理科大学, 理工学部, 助手 (70307700) 渡邉昇東京理科大学, 理工学部, 講師 (70191781) 明石重男新潟大学, 理学部, 助教授 (30202518) 小嶋泉京都大学, 数理解析研究所, 助教授 (60150322)
Keywords	情報力学 / 量子相互エントロピー / 量子コンピュータ / エンタングルド状態 / カオス尺度 / マルチプルアライメント / エントロピー進化率 / 場の理論
Research Abstract	情報力学は,エントロピー理論から端を発した複雑さと力学の融合した理論であり,様々な分野の複雑さを統一的に扱うことができることやその情報の伝達を取り扱うことができるといった特徴を持っている.本年度は,この情報力学の視点から以下のような研究を行った:(1)量子計算では,エンタングルド状態と呼ばれるいくつかの量子状態を重ね合わせた状態を用いるのが特徴となっている.これを用いると因数分解等を高速で行うアルゴリズムを作ることができる.こうしたエンタングルド状態の定式化とそれらの分類を厳密に行った.(2)量子コンピュータに関する研究の一つとして,その光学的モデルとして考案されたFredkin-Toffoli-Milbum(FTM)ゲートにおける状態変化の様子を量子チャネルとして新たに記述し,さらにはその回路の持つ情報伝送の効率を量子相互エントロピー厳密に調べる研究を行った.(3)カオス力学系は情報理論の視点から見ると,複雑な挙動を示すある通信過程と考えることができる.本研究では,情報力学をベースにして新たな尺度(カオス尺度)を導入し,ハイゼンベルグ方程式の時間離散化,古典的なカオス力学系の量子化及び量子系におけるある種の非線形変換等を行うことによって,その対応する量子力学系がカオス的な振る舞いをするかを調べた.(4)患者がAIDSを発症したときに変化すると考えられているCD4値や免疫等の変化の過程を情報力学の複雑さの一つであるカオス尺度を用いて解析し,AIDSの発症時の特徴を調べた.(5)量子場の理論の立場から,量子力学における観測問題やミクロ・マクロ変換の問題に関する研究を行った. 以上の研究を通して,情報力学が内包する統一的なものの捉え方が様々な分野を研究する上で非常に有益であることが再確認された.

Research Products

(27 results)

All Other

All Publications (27 results)

[Publications] M.Ohya: "Complexity and fractal dimonsion for quantum states" Open Systems and Information Dynamics. 4. 141-157 (1997)
[Publications] M.Ohya: "Foundation of entropy,complexity and fractal in quantum systems" Probability Towards 2000. 263-286 (1998)
[Publications] M.Ohya: "Complexities and their applications to characterization of chaos" International Journal of Theoretical Physics. 37. 495-505 (1998)
[Publications] K.Sato,S.Miyazaki,M.Ohya: "Analysis of HIV by entropy evolution rate" Amino Acids. 14. 343-352 (1998)
[Publications] T.Matsuoka,M.Ohya: "Fractal dimension of a state and their application to shape aralyss problem" Chubu Forum for Mathematical Sciences. 4. 15-26 (1998)
[Publications] M.Ohya: "A mathematical foundation of guantum information and quantum comput〓-on quantum entropy and entanglement-" The Proceedings of 3rd International Conference on Computationd Intelliyence and Neuroscience. 2. 209-217 (1998)
[Publications] L.Accardi,M.Ohya: "Compound channels,transition expectations,and littings" Appl.Math.Optim.39. 33-59 (1999)
[Publications] M.Ohya: "Fundamevtals of quantum mutual entropy and capacity" to appear in Open Systems and Information Dynamics.
[Publications] I.Ojima,M.Abe,N.Nakanishi: "Resolution of the BRS-Singlet-Pair Problem in Quantum Einstein" Nucl.Phys.B486. 466-478 (1997)
[Publications] I.Ojima,D.Buchholz: "Spontaneous Collapse of Supersymmetry" Nucl.Phys.B489. 228-242 (1997)
[Publications] I.Ojima: "Spontaneous Collapse of Supersymmetry" to appear in the Proceedings of 2nd Jagna International Workshop.
[Publications] I.Ojima: "Symmetry Breaking Patterns-Spontaneous Collapse of SUSY and Others-" to appear in Classical and Quantum White Noise.
[Publications] S.Akashi: "Superposition representability probleme of guantum information channels" Open Systems and Information Dynamics. 4. 45-52 (1997)
[Publications] S.Akashi: "Quantum entropy thesretic aspects of the 13th problem formulatel by Hilbert" Journal of Ramanujan Mathematical Society. 2. 135-146 (1997)
[Publications] S.Akashi: "Topological classification of nuclear operators and its appliation to the theory of continuously differentiable function spaces" Pan American Mathematical Journal. 8. 89-96 (1998)
[Publications] S.Akashi: "Application of quantum entropy theoretic methods to homeomorphism problems of operator algebros" Reports on Mathematical Physics. 42. 385-388 (1998)
[Publications] M.Ohya,N.Watanabe: "Quantum capacity of noisy quantum channel" Quantum Communication,Computing,and Measurement. 3. 213-220 (1997)
[Publications] L.Accardi,M.Ohya,N.Watanabe: "Dynamical entropy through quantum Markov chain" Open Systeme and Information Dynamics. 4. 71-87 (1997)
[Publications] M.Ohya,D.Petz,N.Watanabe: "On capacities of quantum channels" Probability and Mathematical Statistics. 17. 179-196 (1997)
[Publications] M.Ohya,D.Petz,N.Watanabe: "Numerical computation of guantum capacity" International Journal of Theoretical Physics. 37. 507-510 (1998)
[Publications] M.Ohya,N.Watanabe: "On mathematical treatment of Fredkin-Toffoli-Milburn gate" Physica D. 20. 206-213 (1998)
[Publications] K.Inoue,M.Ohya,H.Suyari: "Characterization of quantum teleportation by nonlinear quantum channel and quantum mutual entropy" Physica D. 20. 117-124 (1998)
[Publications] K.Inoue,M.Ohya: "Chaosdegree and its appliations to quantum dynamical system" The Proceeding of 3rd International Conference on Computational Intelligence and Neuroscience. 2. 167-169 (1998)
[Publications] RS.Ingarden,A.Kossakowski,M.Ohya: "Information Dynamics and Open Systems" Kluwer Academic Publishers, (1997)
[Publications] 大矢雅則,渡邉昇: "量子通信理論の基礎-量子情報から光通信へ-" 牧野書店, (1998)
[Publications] 大矢雅則: "情報進化論" 岩波書店から出版予定,
[Publications] 大矢雅則: "量子情報理論と量子コンピュタ" 丸善出版から出版予定,

1998 Fiscal Year Annual Research Report

情報力学の研究とその数理的応用

Principal Investigator

大矢 雅則 東京理科大学, 理工学部, 教授 (90112896)

Research Products

[Publications] M.Ohya: "Complexity and fractal dimonsion for quantum states" Open Systems and Information Dynamics. 4. 141-157 (1997)

[Publications] M.Ohya: "Foundation of entropy,complexity and fractal in quantum systems" Probability Towards 2000. 263-286 (1998)

[Publications] M.Ohya: "Complexities and their applications to characterization of chaos" International Journal of Theoretical Physics. 37. 495-505 (1998)

[Publications] K.Sato,S.Miyazaki,M.Ohya: "Analysis of HIV by entropy evolution rate" Amino Acids. 14. 343-352 (1998)

[Publications] T.Matsuoka,M.Ohya: "Fractal dimension of a state and their application to shape aralyss problem" Chubu Forum for Mathematical Sciences. 4. 15-26 (1998)

[Publications] M.Ohya: "A mathematical foundation of guantum information and quantum comput〓-on quantum entropy and entanglement-" The Proceedings of 3rd International Conference on Computationd Intelliyence and Neuroscience. 2. 209-217 (1998)

[Publications] L.Accardi,M.Ohya: "Compound channels,transition expectations,and littings" Appl.Math.Optim.39. 33-59 (1999)

[Publications] M.Ohya: "Fundamevtals of quantum mutual entropy and capacity" to appear in Open Systems and Information Dynamics.

[Publications] I.Ojima,M.Abe,N.Nakanishi: "Resolution of the BRS-Singlet-Pair Problem in Quantum Einstein" Nucl.Phys.B486. 466-478 (1997)

[Publications] I.Ojima,D.Buchholz: "Spontaneous Collapse of Supersymmetry" Nucl.Phys.B489. 228-242 (1997)

[Publications] I.Ojima: "Spontaneous Collapse of Supersymmetry" to appear in the Proceedings of 2nd Jagna International Workshop.

[Publications] I.Ojima: "Symmetry Breaking Patterns-Spontaneous Collapse of SUSY and Others-" to appear in Classical and Quantum White Noise.

[Publications] S.Akashi: "Superposition representability probleme of guantum information channels" Open Systems and Information Dynamics. 4. 45-52 (1997)

[Publications] S.Akashi: "Quantum entropy thesretic aspects of the 13th problem formulatel by Hilbert" Journal of Ramanujan Mathematical Society. 2. 135-146 (1997)

[Publications] S.Akashi: "Topological classification of nuclear operators and its appliation to the theory of continuously differentiable function spaces" Pan American Mathematical Journal. 8. 89-96 (1998)

[Publications] S.Akashi: "Application of quantum entropy theoretic methods to homeomorphism problems of operator algebros" Reports on Mathematical Physics. 42. 385-388 (1998)

[Publications] M.Ohya,N.Watanabe: "Quantum capacity of noisy quantum channel" Quantum Communication,Computing,and Measurement. 3. 213-220 (1997)

[Publications] L.Accardi,M.Ohya,N.Watanabe: "Dynamical entropy through quantum Markov chain" Open Systeme and Information Dynamics. 4. 71-87 (1997)

[Publications] M.Ohya,D.Petz,N.Watanabe: "On capacities of quantum channels" Probability and Mathematical Statistics. 17. 179-196 (1997)

[Publications] M.Ohya,D.Petz,N.Watanabe: "Numerical computation of guantum capacity" International Journal of Theoretical Physics. 37. 507-510 (1998)

[Publications] M.Ohya,N.Watanabe: "On mathematical treatment of Fredkin-Toffoli-Milburn gate" Physica D. 20. 206-213 (1998)

[Publications] K.Inoue,M.Ohya,H.Suyari: "Characterization of quantum teleportation by nonlinear quantum channel and quantum mutual entropy" Physica D. 20. 117-124 (1998)

[Publications] K.Inoue,M.Ohya: "Chaosdegree and its appliations to quantum dynamical system" The Proceeding of 3rd International Conference on Computational Intelligence and Neuroscience. 2. 167-169 (1998)

[Publications] RS.Ingarden,A.Kossakowski,M.Ohya: "Information Dynamics and Open Systems" Kluwer Academic Publishers, (1997)

[Publications] 大矢雅則,渡邉 昇: "量子通信理論の基礎-量子情報から光通信へ-" 牧野書店, (1998)

[Publications] 大矢雅則: "情報進化論" 岩波書店から出版予定,

[Publications] 大矢雅則: "量子情報理論と量子コンピュタ" 丸善出版から出版予定,

大矢雅則東京理科大学, 理工学部, 教授 (90112896)

[Publications] 大矢雅則,渡邉昇: "量子通信理論の基礎-量子情報から光通信へ-" 牧野書店, (1998)