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量子ジャンプによる誤りを考慮した量子符号の組合せ論的構成法

Research Project

Project/Area Number 20654012
Research Category

Grant-in-Aid for Challenging Exploratory Research

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

Principal Investigator

神保 雅一  名古屋大学, 大学院・情報科学研究科, 教授 (50103049)

Co-Investigator(Kenkyū-buntansha) 城本 啓介  熊本大学, 自然科学研究科, 教授 (00343666)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2010: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2009: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2008: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords離散数学 / 情報通信工学 / 量子符号 / 量子ジャンプ符号 / 組合せデザイン / t-SEED / 5-デザイン / large set / 5-design / disjoint
Research Abstract

量子ジャンプ符号は量子の自然減衰によって起こる量子ジャンプがもたらす記憶誤りを訂正するために導入された.H22年度は量子ジャンプ符号の組合せ論的定式化を行い,その上限界式の評価および有限アフィン平面から生成される2-デザインの分解を用いて量子ジャンプ符号を構成する研究を行った.
(1) 量子ジャンプ符号の組合せ論的定義とその上限界式の改良
量子ジャンプ符号の定義は複雑で数学的にその組合せ構造を明示することは容易ではなかった.本研究では,Mutually orthogonal partial t-design(t-MOD)と呼ばれる組合せ構造を導入し,その組合せ構造が量子ジャンプ符号と同値であることを明らかにした.さらにt-MODのデザインの数に関する上限界式を精査し,あるパラメータの場合には上限界式を極端に改良できることを示し,改良された上限界を与えるt-MODの存在を調べた.この結果の一部を,Croatiaでの国際会議で3時間におよぶ招待講演で公表した.
(2) 有限アフィン幾何を用いる構成法:有限アフィン幾何AG(n,q)の平面の集合は2-designをなすことが古くから知られているが,そのブロック集合を複数の部分集合に分割することにより,q=2,3の場合に,会合数が小さい複数の2-designに分割されることを示した.この結果,新たなt-MODが構成できることを示した.

Report

(3 results)
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (29 results)

All 2011 2010 2009 2008 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (16 results) Book (2 results)

  • [Journal Article] Unifying some known infinite families of combinatoria1 3-designs2010

    • Author(s)
      M.Jimbo, Y.Kunihara, R.Laue, M.Sawa
    • Journal Title

      Journal of Combinatorial Theory, Ser. A

      Volume: 118 Pages: 1072-1085

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of mutually disjoint Steiner systems from isomorphic Golay codes.2009

    • Author(s)
      M.Jimbo, K.Shiromoto
    • Journal Title

      J. Combinatorial Theory, Ser. A Vol. 116

      Pages: 1245-1251

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sets of frequency hopping sequences : bounds and optimal constructions2009

    • Author(s)
      C.Ding, R.Fuji-Hara, Y.Fijiwara, M.Jimbo, M.Mishima
    • Journal Title

      IEEE Transactions on Information Theory Vol. 55

      Pages: 3297-3304

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of disjoint Steiner systems from isomorphic Golay codes2009

    • Author(s)
      M. Jimbo, K. Shiromoto
    • Journal Title

      J. Combinatorial Theory, Ser. A (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Mac Williams type identity for matroids2008

    • Author(s)
      T. Britz, K. Shiromoto
    • Journal Title

      Discrete Mathematics 308

      Pages: 4551-4559

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of OA(s^t, t+1, s, t) by nonlinear functions and someclassification for s=42008

    • Author(s)
      S. Yagi, K. Mimura, M. Jimbo
    • Journal Title

      Journal of Statistical Planning and Inference Vol. 138 No. 11

      Pages: 3309-3315

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compatibility of BIB designs2008

    • Author(s)
      M. Sawa, S. Kageyama, M. Jimbo
    • Journal Title

      Statistics and Applications Vol. 6 No. 1, 2

      Pages: 56-71

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some constructions for block sequences for Steiner quadruple systems with error correcting consecutive unions2008

    • Author(s)
      K. Momihara, M. Jimbo
    • Journal Title

      Journal of Combinatorial Designs Vol. 16

      Pages: 152-163

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Further constructions for BIB designs with nested rows and columns2008

    • Author(s)
      T. Hishida, M. Jimbo, M. Mishimai, K. Ozawa, Y. Mutoh
    • Journal Title

      Ars Combinatoria Vol. 86

      Pages: 239-256

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A newseries of main effects plus one plan for 2^m factorial experiments with m=4λ+1 and 2m runs

    • Author(s)
      N.Esmailzadeh, H, Talebi, K.Momihara, M.Jimbo
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 印刷中

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mutually disjoint 5-designs from Pless symmetry codes

    • Author(s)
      M.Angata, K.Shiromoto
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: 印刷中

    • NAID

      120005399999

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 量子情報理論と組合せデザイン2011

    • Author(s)
      城本啓介
    • Organizer
      RIMS共同研究「代数的符号理論、組合せデザインとその周辺」
    • Place of Presentation
      京都大学、京都
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 符号とマトロイドにおける双対性2010

    • Author(s)
      城本啓介
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学、滋賀
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Recursive constructions of t-SEEDs related to quantum jump codes2010

    • Author(s)
      林恰伶, 神保雅一
    • Organizer
      研究集会「実験計画法およびその周辺領域における組合せ構造の解明とその応用」
    • Place of Presentation
      兵庫県城崎
    • Year and Date
      2010-11-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Formula of channel matrix for coded quantum signals by classical linear codes over Zm2010

    • Author(s)
      M.Ota, K.Shiromoto
    • Organizer
      2010 International Symposium on Information Theory and Its Applications
    • Place of Presentation
      Taichung, Taiwan
    • Year and Date
      2010-10-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Analytical expression of s-th power of Gram matrix for group covariant signals and its application2010

    • Author(s)
      T.S.Usuda, K.Shiromoto
    • Organizer
      The Tenth International Conference on Quantum Communication, Measurement and Computation
    • Place of Presentation
      University of Queensland, Australia
    • Year and Date
      2010-07-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Quantum jump codes and related combinatorial designs2010

    • Author(s)
      M.Jimbo
    • Organizer
      Information Security, Coding Theory and Related Combinatorics
    • Place of Presentation
      Opatia, Croatia
    • Year and Date
      2010-06-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a strictly cyclcic SQSs admitting all units as its multipliers2009

    • Author(s)
      神保雅一
    • Organizer
      研究集会「組合せデザイン理論とその応用」
    • Place of Presentation
      ウェルシティ湯河原(静岡県)
    • Year and Date
      2009-08-31
    • Related Report
      2009 Annual Research Report
  • [Presentation] 種々の性質をもつ3-デザインの構成法とその応用2009

    • Author(s)
      国原雄太、澤正憲、神保雅一
    • Organizer
      2009年度応用数学合同研究集会
    • Place of Presentation
      滋賀
    • Related Report
      2009 Annual Research Report
  • [Presentation] A strictly cyclic Steiner quadruple system on Z_v admitting all units as multipliers2008

    • Author(s)
      M. Jimbo, K. Momihara, S. Yoshikawa
    • Organizer
      The 4th International Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      ニュージーランド、オークランド大学
    • Year and Date
      2008-12-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Pless symmetry codeから構成される互いに排反な組合せデザイン2008

    • Author(s)
      安形昌幸, 城本啓介
    • Organizer
      2008年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      2008-12-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] A Steiner quadruple systems on Z_p^m admitting all units as multipliers2008

    • Author(s)
      M. Jimbo
    • Organizer
      Combinatorial Design Theory, 招待講演
    • Place of Presentation
      カナダ、Banff, Int. Research Station
    • Year and Date
      2008-11-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Quantum jump codeと組合せデザイン2008

    • Author(s)
      神保雅一, 城本啓介
    • Organizer
      代数的符号理論と組合せデザイン
    • Place of Presentation
      京都大学、数理解析研
    • Year and Date
      2008-10-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] 自己双対符号から構成されるt-SEEDについて2008

    • Author(s)
      城本啓介, 神保雅一
    • Organizer
      RIMS共同研究「代数的符号理論と組合せデザイン」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-10-14
    • Related Report
      2008 Annual Research Report
  • [Presentation] デザイン構造をもつマトロイド2008

    • Author(s)
      城本啓介
    • Organizer
      研究集会「離散数学の統計科学および関連分野への応用」
    • Place of Presentation
      ホテルくさかベアルメリア(岐阜)
    • Year and Date
      2008-08-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] 互いに素な組合せデザインについて2008

    • Author(s)
      安形昌幸, 城本啓介
    • Organizer
      純粋数学及び用数学としての組合せ論・離散数学そしてその周辺ワークショップ
    • Place of Presentation
      電気通信大学
    • Year and Date
      2008-07-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] A Wei type duality theorem for matroids2008

    • Author(s)
      城本啓介
    • Organizer
      第25回代数的組合せ論シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-06-24
    • Related Report
      2008 Annual Research Report
  • [Book] Information Security, Coding Theory and Related Combinatorics, Chapter13 : Quantum jump codes and related combinatorial designs2011

    • Author(s)
      M.Jimbo, K.Shiromoto
    • Total Pages
      451
    • Publisher
      IOS Press
    • Related Report
      2010 Annual Research Report
  • [Book] 新インターユニバーシティ暗号とセキュリティ2010

    • Author(s)
      神保雅一編著(三嶋美和子,城本圭介含, 他8名)
    • Total Pages
      177
    • Publisher
      オーム社
    • Related Report
      2010 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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