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Information theory based on general probabilistic theories and its application to the foundation of quantum mechanics

Research Project

Project/Area Number 17K18107
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Theory of informatics
Mathematical physics/Fundamental condensed matter physics
Research InstitutionShibaura Institute of Technology

Principal Investigator

Kimura Gen  芝浦工業大学, システム理工学部, 教授 (80517011)

Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords量子力学基礎論 / 量子情報理論 / 一般確率論 / 量子開放系理論 / ベルの定理 / 情報理論 / 量子力学の原理 / 完全正値性 / ベル定理 / 量子力学 / 相対論的情報理論 / 量子力学の原理的特徴づけ
Outline of Final Research Achievements

We investigated the foundations of quantum theory and quantum information theory mainly based on general probabilistic theories. We clarified the universal relationship between the geometrical structure of the state space and information storing, and provided an information-theoretic understanding of simple questions such as why only qubit systems have point symmetry (Bloch Ball). In addition, the principle of information symmetry was developed and various information quantities were characterized based on general probabilistic theories. We also discovered the universal law of relaxation times for completely positive dynamics and a new relaxed Bell's inequality by introducing a hiddeness which characterizes the extent how much we need a hidden variable. Quantum teleportation based on the vacuum entanglement was also studied where we have clarified the optimal procol with a given entanglement.

Academic Significance and Societal Importance of the Research Achievements

近年量子情報科学の発展を受けて,情報理論的な量子力学の理解の可能性が高まっている.従来は道具主義的な理解しかできていなかった量子物理学に新たな光を当てることになり,より深い理解につながることが期待される.また,様々な情報処理や物理法則の間の連関性の理解が深まり,新たな応用につながることも期待できる.例えば,我々の成果により状態空間の幾何学構造から,物理系の情報蓄積量が見積もれるようになった.また,量子開放系の研究は,量子コンピュータなどの実現の最大の障壁であるデコヒーレンスの理解を深めることになった.これらの研究は,自然観の在り方を探る基礎から情報科学への応用まで幅広い意義を持っている.

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (21 results)

All 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 6 results,  Open Access: 1 results) Presentation (13 results) (of which Int'l Joint Research: 6 results,  Invited: 6 results) Remarks (1 results)

  • [Int'l Joint Research] Nicolaus Copernicus University(ポーランド)

    • Related Report
      2021 Annual Research Report
  • [Journal Article] Bounding the Frobenius norm of a q-deformed commutator2022

    • Author(s)
      Dariusz Chruscinski, Gen Kimura, Hiromichi Ohno, Tanmay Singal
    • Journal Title

      Linear Algebra and its Applications

      Volume: 646 Pages: 95-106

    • DOI

      10.1016/j.laa.2022.03.021

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Constraints for the spectra of generators of quantum dynamical semigroups2021

    • Author(s)
      Dariusz Chruscinski, Ryohei Fujii, Gen Kimura, Hiromichi Ohno
    • Journal Title

      Linear Algebra and its Applications

      Volume: 630 Pages: 293-305

    • DOI

      10.1016/j.laa.2021.08.012

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup2021

    • Author(s)
      Dariusz Chruscinski, Gen Kimura, Andrzej Kossakowski, and Yasuhito Shishido
    • Journal Title

      Physical Review Letters

      Volume: 127 Issue: 5 Pages: 050401-050401

    • DOI

      10.1103/physrevlett.127.050401

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Entanglement extracted from vacuum into accelerated Unruh-DeWitt detectors and energy conservation2019

    • Author(s)
      Jun-ichirou Koga, Kengo Maeda, and Gen Kimura
    • Journal Title

      Physical Review D

      Volume: 100 Issue: 6 Pages: 065013-065013

    • DOI

      10.1103/physrevd.100.065013

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Quantum teleportation in vacuum using only Unruh-DeWitt detectors2018

    • Author(s)
      Jun-ichirou Koga, Gen Kimura, and Kengo Maeda
    • Journal Title

      Physical Review A

      Volume: 97 Issue: 6

    • DOI

      10.1103/physreva.97.062338

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Universal Constraints on Relaxation Times for d-Level GKLS Master Equations2017

    • Author(s)
      Kimura, G., Ajisaka, S. & Watanabe, K.
    • Journal Title

      Open Systems and Information Dynamics

      Volume: 24 Issue: 04 Pages: 1740009-1740009

    • DOI

      10.1142/s1230161217400091

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Universal Constraints on relaxation rates for open quantum Markovian dynamics2022

    • Author(s)
      Gen Kimura
    • Organizer
      YITP international workshop on quantum information entropy in physics
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非因果的局所量子論に基づく非適応測定による測定型量子計算2022

    • Author(s)
      高桑颯希, 原田悠佑, 木村元
    • Organizer
      物理学会 第77回年次大会(2021年)
    • Related Report
      2021 Annual Research Report
  • [Presentation] Universal constraint for relaxation rates of quantum dynamical semigroups II: Based on r-function approach2021

    • Author(s)
      Gen Kimura
    • Organizer
      Two-Day Workshop to celebrate the 60th anniversary of the paper on dynamical maps by E. C. G. Sudarshan, P. M. Mathews and J. Rau
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Universal constraint for relaxation rates for quantum dynamical semigroup - physical manifestation of completely positive condition2021

    • Author(s)
      Gen Kimura
    • Organizer
      52 Symposium on Mathematical Physics
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 情報対称性の原理は量子論を特徴づけられるか?2021

    • Author(s)
      永石健人, 木村元
    • Organizer
      日本物理学会第76回年次大会(2021)
    • Related Report
      2020 Research-status Report
  • [Presentation] 測定非独立性を考慮したBell-CHSH不等式の一般化2021

    • Author(s)
      鱸優吾, 木村元
    • Organizer
      日本物理学会第76回年次大会(2021)
    • Related Report
      2020 Research-status Report
  • [Presentation] Universal constraints on relaxation times of GKLS master equations2020

    • Author(s)
      Gen Kimura, Yasuto Shishido, Dariusz Chruscinski, Andrzej Kossakowski
    • Organizer
      "020 International Workshop on Quantum Information, Quantum Computing and Quantum Control"
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 一般確率論における情報対称性の考察2020

    • Author(s)
      永石健人, 木村元
    • Organizer
      第75回年次大会(2020年)
    • Related Report
      2019 Research-status Report
  • [Presentation] GKLSマスター方程式における緩和時間の普遍則2020

    • Author(s)
      木村元
    • Organizer
      量子論の諸問題と今後の発展
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Informational origin of point-asymmetry of state space in general probabilistic theories2018

    • Author(s)
      Gen Kimura
    • Organizer
      50 Symposium on Mathematical Physics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 一般確率論における情報取得量の下限2018

    • Author(s)
      深沢幸希, 木村元
    • Organizer
      日本物理学会 2018年年次大会
    • Related Report
      2017 Research-status Report
  • [Presentation] 状態空間の点非対称性の情報理論的起源 一般確率論の観点から2018

    • Author(s)
      木村元, 松本啓史
    • Organizer
      日本物理学会 2018年年次大会
    • Related Report
      2017 Research-status Report
  • [Presentation] Information storing yields a point asymmetry of state space2017

    • Author(s)
      Gen Kimura
    • Organizer
      Quantum Information Theory and Mathematical Physics 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] 一般確率論における情報蓄積量と状態空間(点)対称性の関係

    • URL

      https://arxiv.org/abs/1802.01162

    • Related Report
      2020 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2023-01-30  

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