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The Weak Value and the Weak Measurement: their Foundation and Application

Research Project

Project/Area Number 25400423
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Atomic/Molecular/Quantum electronics
Research InstitutionHigh Energy Accelerator Research Organization

Principal Investigator

TSUTSUI Izumi  大学共同利用機関法人高エネルギー加速器研究機構, 素粒子原子核研究所, 准教授 (10262106)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords弱値 / 弱測定 / 不確定性関係 / 相補性 / 精密測定 / 擬確率 / 量子推定 / 量子測定 / 波動と粒子の二重性 / 物理量の実在性
Outline of Final Research Achievements

In the present research, we have succeeded to show that the Weak Value, which has been intensively studied in recent years as a novel physical quantity in quantum mechanics, may be regarded as a local realistic quantity in the typical quantum mechanical particle-wave duality viewpoint. We also derived a new uncertainty relation for the Weak Value, which includes the standard Heisenberg uncertainty relation as a special case. In addition, we have also provided a theoretical model allowing us to examine the validity of precision measurement by using the Weak Measurement, which is a method to obtain the Weak Value by means of conditional quantum measurement. With this, we analyzed some well-known examples of such precision measurement (including the detection of the quantum Hall effect of light) and proved their validity on a firm basis.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (35 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (9 results) (of which Peer Reviewed: 9 results,  Acknowledgement Compliant: 4 results,  Open Access: 2 results) Presentation (23 results) (of which Invited: 6 results)

  • [Int'l Joint Research] Tel Aviv University(Israel)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] ウィーン工科大学(オーストリア)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] テルアヴィヴ大学(イスラエル)

    • Related Report
      2015 Research-status Report
  • [Journal Article] A General Framework of Quasi-probabilities and the Statistical Behaviour of Non-commuting Quantum Observables2018

    • Author(s)
      J. Lee, I. Tsutsui
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak Value, Quasiprobability and Bohmian Mechanics2017

    • Author(s)
      Kazuki Fukuda, Jaeha Lee, Izumi Tsutsui
    • Journal Title

      Found. Phys.

      Volume: 47 Issue: 2 Pages: 236-255

    • DOI

      10.1007/s10701-016-0054-3

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Quasi-probabilities in Conditioned Quantum Measurement and a Geometric/Statistical Interpretation of Aharonov's Weak Value2017

    • Author(s)
      Jaeha Lee, Izumi Tsutsui
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: 052A01 Issue: 5 Pages: 1-146

    • DOI

      10.1093/ptep/ptx024

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Uncertainty Relations for Approximation and Estimation2016

    • Author(s)
      Jaeha Lee, Izumi Tsutsui
    • Journal Title

      Phys. Lett. A

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Weak Value and Wave-Particle Duality2015

    • Author(s)
      T. Mori, and I. Tsutsui
    • Journal Title

      Quant. Stud.: Math. Found.

      Volume: なし Issue: 4 Pages: 371-378

    • DOI

      10.1007/s40509-015-0039-5

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Quantum Trajectories based on the Weak Value2015

    • Author(s)
      Takuya Mori, Izumi Tsutsui
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: 043A01 Issue: 4 Pages: 1-19

    • DOI

      10.1093/ptep/ptv032

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Yet Another Introduction to Postselected Measurements2015

    • Author(s)
      J. Lee, and I. Tsutsui
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: なし

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Merit of Amplification by Weak Measurement in View of Measurement Uncertainty2014

    • Author(s)
      Jaeha Lee, Izumi Tsutsui
    • Journal Title

      Quantum Studies: Mathematics and Foundations

      Volume: 1

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Complex Probability Measure and Aharonov's Weak Value2013

    • Author(s)
      Tatsuya Morita, Toshihiko Sasaki, Izumi Tsutsui
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: 3

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 弱値と量子測定: ABL規則の 解釈と混合状態における弱値2018

    • Author(s)
      筒井 泉
    • Organizer
      研究会「量子測定の物理と情報通信」
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 量子力学の時間対称形式に おけるABL規則について2017

    • Author(s)
      筒井泉
    • Organizer
      「量子測定の物理と情報通信」研究会
    • Place of Presentation
      東北大学(宮城県・仙台市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 近似/推定の不確定性関係2016

    • Author(s)
      李宰河, 筒井泉
    • Organizer
      日本物理学会 第71回年次大会
    • Place of Presentation
      東北学院大(宮城県仙台市)
    • Year and Date
      2016-03-22
    • Related Report
      2015 Research-status Report
  • [Presentation] 弱値の基礎にある擬確率と不確定性関係2016

    • Author(s)
      李宰河, 筒井泉
    • Organizer
      KEK研究会「量子論諸問題と今後の発展」(QMKEK6)
    • Place of Presentation
      高エネルギー加速器研究機構(茨城県つくば市)
    • Year and Date
      2016-02-17
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 弱測定から見えてくる物理2016

    • Author(s)
      筒井泉
    • Organizer
      日本物理学会2016年秋期大会
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 弱値増幅を用いた光のスピンホール効果の測定不確かさについて2015

    • Author(s)
      森澤教有, 李宰河, 筒井泉
    • Organizer
      第33回量子情報技術研究会(QIT33)
    • Place of Presentation
      NTT厚木研究開発センター(神奈川県厚木市)
    • Year and Date
      2015-11-24
    • Related Report
      2015 Research-status Report
  • [Presentation] 弱値から見る不確定性関係2015

    • Author(s)
      李宰河, 筒井泉
    • Organizer
      2015年 秋季大会
    • Place of Presentation
      関西大(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] de Brogile - Bohm 理論と擬確率ならびに実在の概念2015

    • Author(s)
      福田教紀, 筒井泉, 李宰河
    • Organizer
      2015年 秋季大会
    • Place of Presentation
      関西大(大阪府吹田市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] 擬確率分布の条件付き期待値としての「弱値」について2015

    • Author(s)
      李宰河, 筒井泉
    • Organizer
      第32回量子情報技術研究会(QIT32)
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2015-05-26
    • Related Report
      2015 Research-status Report
  • [Presentation] 「弱測定」を用いた「複素確率測度」の測定について2015

    • Author(s)
      李宰河,筒井泉
    • Organizer
      日本物理学会 第70回年次大会
    • Place of Presentation
      早稲田大
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] 量子力学の圏論的側面2015

    • Author(s)
      松久勝彦,筒井泉
    • Organizer
      日本物理学会 第70回年次大会
    • Place of Presentation
      早稲田大
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Basics of the Weak Value ! and the Weak Measurement2015

    • Author(s)
      筒井泉
    • Organizer
      International Workshop on Weak Value and Weak Measurement
    • Place of Presentation
      東京工大
    • Year and Date
      2015-03-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Foundations of the Weak Value Revisted: its Reality, Interpretation and Probability2015

    • Author(s)
      筒井泉
    • Organizer
      Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory
    • Place of Presentation
      名古屋大
    • Year and Date
      2015-03-09
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 不確かな量子測定の数学的記述とその応用について2014

    • Author(s)
      李宰河,森田辰弥,筒井泉
    • Organizer
      日本物理学会 2014年秋季大会
    • Place of Presentation
      中部大
    • Year and Date
      2014-10-09
    • Related Report
      2014 Research-status Report
  • [Presentation] 物理量の同時測定可能性について2014

    • Author(s)
      福田教紀,筒井泉,森田辰弥,李宰河
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 量子干渉における弱値の意味2014

    • Author(s)
      森琢也,筒井泉
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 事後選択の技術の有用性に関する推定理論的考察2014

    • Author(s)
      李宰河,森田辰弥,筒井泉
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 物理量の実在性と弱値2014

    • Author(s)
      筒井泉
    • Organizer
      量子論の諸問題と今後の発展
    • Place of Presentation
      高エネルギー加速器研究機構(KEK)研究本館
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 弱値の解釈と弱測定の精密測定への応用について2014

    • Author(s)
      筒井泉, 森田辰弥, 森琢也, 李宰河
    • Organizer
      第30回量子情報技術研究会 (QIT30)
    • Place of Presentation
      名古屋大学 トヨタ講堂
    • Related Report
      2013 Research-status Report
  • [Presentation] 弱値による粒子の「軌跡」について2013

    • Author(s)
      森琢也,筒井泉
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 連続した弱値の測定誤差について2013

    • Author(s)
      森田辰弥,李宰河,筒井泉
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 弱値および弱測定の一般確率論による定式化2013

    • Author(s)
      福田教紀,筒井泉,森田辰弥,李宰河
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 「弱値」の測定モデルの一般化について2013

    • Author(s)
      李宰河,森田辰弥,筒井泉
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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