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New developments in quantum measurement theory based on the Heisenberg picture

Research Project

Project/Area Number 16K17641
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionNagoya University

Principal Investigator

Okamura Kazuya  名古屋大学, 情報学研究科, 特任助教 (90725178)

Research Collaborator Ozawa Masanao  
Ojima Izumi  
Saigo Hayato  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords量子測定 / Heisenberg描像 / 測定スキーム / 完全正値インストルメント / 対称性 / 測定過程 / リー群 / 不確定性関係 / ドレスト光子 / 微分代数 / 量子測定理論 / C^*-代数 / セクター / 測定相関の系 / 情報基礎
Outline of Final Research Achievements

Quantum measurement theory is a theory that analyzes the influence of measurement in quantum systems in conjunction with measurement data. We made the theory applicable to quantum field theory and "dressed photons" generated by interaction of the electromagnetic field with matter fields on sub-wavelength scales. We also advanced a characterization of measurement at the level of correlation. We also mathematically studied modeling of measurement using the theory of operator algebras (especially C*-algebras), differential algebras and infinite dimensional Lie groups.

Academic Significance and Societal Importance of the Research Achievements

量子測定理論の適用領域拡大に貢献することができた。長い歴史的経緯もあるためこれまで量子力学的な観点から測定による状態変化の記述に関する研究が大部分を占めてきた。今回,量子場理論や,電磁場が波長未満のスケールで物質場と相互作用することで生じる「ドレスト光子」に対して測定理論を適用可能にした一方で,相関のレベルでの測定の特徴づけを前進させた。測定という実験においてある意味で“当たり前”に関与する物理過程に対する理解を微々たるものであるが深められた意義は(今後の研究次第ではあるが)確かにあると考える。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (18 results)

All 2019 2018 2017 2016

All Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 4 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results)

  • [Journal Article] Measuring Processes and the Heisenberg Picture2018

    • Author(s)
      Okamura Kazuya
    • Journal Title

      -

      Volume: - Pages: 361-396

    • DOI

      10.1007/978-981-13-2487-1_14

    • ISBN
      9789811324864, 9789811324871
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Approach from Measurement Theory to Dressed Photon2018

    • Author(s)
      Okamura Kazuya
    • Journal Title

      -

      Volume: - Pages: 137-167

    • DOI

      10.1007/978-3-319-98267-0_5

    • ISBN
      9783319982663, 9783319982670
    • Related Report
      2018 Annual Research Report
  • [Journal Article] Scalable photonic reinforcement learning by time-division multiplexing of laser chaos2018

    • Author(s)
      Naruse Makoto、Mihana Takatomo、Hori Hirokazu、Saigo Hayato、Okamura Kazuya、Hasegawa Mikio、Uchida Atsushi
    • Journal Title

      Scientific Reports

      Volume: 8 Issue: 1 Pages: 1-16

    • DOI

      10.1038/s41598-018-29117-y

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Why is the environment important for decision making? Local reservoir model for choice-based learning2018

    • Author(s)
      Naruse Makoto、Yamamoto Eiji、Nakao Takashi、Akimoto Takuma、Saigo Hayato、Okamura Kazuya、Ojima Izumi、Northoff Georg、Hori Hirokazu
    • Journal Title

      PLOS ONE

      Volume: 13 Issue: 10 Pages: e0205161-e0205161

    • DOI

      10.1371/journal.pone.0205161

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 量子測定理論の数理2017

    • Author(s)
      岡村和弥
    • Journal Title

      数理解析研究所講究録

      Volume: 2059 Pages: 103-112

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] Category Theory Approach to Solution Searching Based on Photoexcitation Transfer Dynamics2017

    • Author(s)
      Naruse Makoto、Aono Masashi、Kim Song-Ju、Saigo Hayato、Ojima Izumi、Okamura Kazuya、Hori Hirokazu
    • Journal Title

      Philosophies

      Volume: 2 Issue: 3 Pages: 16-16

    • DOI

      10.3390/philosophies2030016

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Local state and sector theory in local quantum physics2016

    • Author(s)
      Izumi Ojima, Kazuya Okamura, Hayato Saigo
    • Journal Title

      Letters in Mathematical Physics

      Volume: 106

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Quantum theory starting from transition probability2016

    • Author(s)
      岡村 和弥
    • Journal Title

      数理解析研究所講究録

      Volume: 2010

    • Related Report
      2016 Research-status Report
  • [Presentation] ドレスト光子と量子場2019

    • Author(s)
      岡村 和弥
    • Organizer
      第66回応用物理学会春季学術講演会
    • Related Report
      2018 Annual Research Report
  • [Presentation] A C*-algebraic approach to quantum measurement2018

    • Author(s)
      岡村 和弥
    • Organizer
      量子場の数理とその周辺
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] A categorical approach to quantum measurement2018

    • Author(s)
      Kazuya Okamura
    • Organizer
      International Symposium on Nonlinear Theory and Its Applications (NOLTA2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 測定理論からのドレスト光子へのアプローチ2018

    • Author(s)
      岡村 和弥
    • Organizer
      第79回応用物理学会秋季学術講演会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Measuring processes and uncertainty relations in general quantum systems2017

    • Author(s)
      岡村 和弥
    • Organizer
      量子情報理論に関連した作用素環論における諸問題の研究
    • Place of Presentation
      京都大学
    • Year and Date
      2017-02-01
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Uncertainty Relations in General Quantum Systems2017

    • Author(s)
      Kazuya Okamura
    • Organizer
      Foundations of Quantum Mechanics and Technology (FQMT)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 測定理論によるドレスト光子のモデリング2017

    • Author(s)
      岡村和弥
    • Organizer
      ドレスト光子の関連技術推進の為の基礎的数理研究
    • Related Report
      2017 Research-status Report
  • [Presentation] 量子測定理論の数理2016

    • Author(s)
      岡村 和弥
    • Organizer
      量子システム推定の数理
    • Place of Presentation
      京都大学
    • Year and Date
      2016-10-26
    • Related Report
      2016 Research-status Report
  • [Presentation] On a mathematical treatment of measurement correlations2016

    • Author(s)
      岡村 和弥
    • Organizer
      量子場の数理とその周辺
    • Place of Presentation
      九州大学
    • Year and Date
      2016-06-06
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 測定相関の一般的扱いについて2016

    • Author(s)
      岡村 和弥
    • Organizer
      第34回量子情報技術研究会 (QIT34)
    • Place of Presentation
      高知工科大学
    • Year and Date
      2016-05-30
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2020-03-30  

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