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Advances in optimal design of nonlinear experiments based on quantum information geometry

Research Project

Project/Area Number 21K11749
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60010:Theory of informatics-related
Research InstitutionThe University of Electro-Communications

Principal Investigator

Suzuki Jun  電気通信大学, 大学院情報理工学研究科, 准教授 (70565332)

Project Period (FY) 2021-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2023: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2021: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords量子状態推定 / 非線形最適実験計画法 / 量子情報幾何 / 量子ベイス推定 / 最適な測定 / 量子Fisher計量 / 量子推定 / 量子ベイズ推定 / 最適実験計画法 / 量子情報幾何学 / 量子推定理論 / 局所最適デザイン / ベイズ最適デザイン
Outline of Research at the Start

本研究では、観測者が統計データを得るための測定の自由度を導入し、各々の測定に対して、条件付き確率分布として統計モデルが1つ定まるという非線形実験計画法における情報幾何学の開拓を行う。目的の1つ目は、与えられた最適基準に対してモデルパラメータを推定するための最適なデザインを求めることである。特に、情報幾何学的なアプローチにより統計モデルの大域的な性質を明らかにすることを目標とする。本研究課題の目的の2つ目は、量子力学によって記述される数理モデルを扱う量子情報理論・量子統計理論における情報幾何学(量子情報幾何学)の開拓である。研究成果からは、数理工学・量子情報科学における基礎的な貢献が期待される。

Outline of Final Research Achievements

The aim of this project is to develop the general framework to discuss the differential geometrical analysis on the theory of optimal design of non-linear experiments. Based on techniques in quantum information geometry, we obtain optimal or near optimal estimation strategies for quantum estimation problems. The more detailed main results out of this project are as follows. 1. Derivation of lower bounds for the Bayesian risk in quantum estimation. 2. Implementation of numerical algorithms to obtain optimal designs. 3. Investigation of the necessary and sufficient condition for saturating the quantum Cramer-Rao inequality. 4. Tradeoff relation for estimating the position of a relativistic spin-1/2 particle. 5. Optimal quantum decoding method for label classification problems using quantum neural network. 6. Properties of the gap between a finite-sample estimation error bound and the asymptotic bound.

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた成果は、量子情報幾何学的なアプローチを取ることにより、従来の実験計画法では議論されなかった、より一般の統計モデルに対する最適なデザインの設計を可能にする理論の構築である。本研究では、最適なデザインを効率的に求める方法の探究を行い、得られた研究成果を現在の実験技術でも実装可能な物理系を用いた精密測定法へと応用する。
本研究成果の意義とは、情報幾何学と非線形最適実験計画法の相互作用により、最適なデザインを効率的に求める方法の探究、新しい数理統計学の理論の枠組みの発展、という数理工学・量子情報科学における基礎的な貢献である。

Report

(4 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (32 results)

All 2024 2023 2022 2021 Other

All Int'l Joint Research (5 results) Journal Article (5 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results,  Open Access: 3 results) Presentation (22 results) (of which Int'l Joint Research: 10 results,  Invited: 5 results)

  • [Int'l Joint Research] オーストラリア国立大学(オーストラリア)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Agency for Sci Tech and Research(シンガポール)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Centre for Quantum Computation, ANU/Department of Quantum Science, ANU(オーストラリア)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Centre for Quantum Technologies,NUS(シンガポール)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Australian National University(オーストラリア)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem2024

    • Author(s)
      SUZUKI Jun
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E107.A Issue: 3 Pages: 510-518

    • DOI

      10.1587/transfun.2023TAP0014

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2024-03-01
    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Error tradeoff relation for estimating the unitary-shift parameter of a relativistic spin-1/2 particle2024

    • Author(s)
      Shin Funada and Jun Suzuki
    • Journal Title

      Physical review A

      Volume: 109 Issue: 1 Pages: 012425-012425

    • DOI

      10.1103/physreva.109.012425

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] QestOptPOVM: An iterative algorithm to find optimal measurements for quantum parameter estimation2024

    • Author(s)
      Jianchao Zhang, Jun Suzuki
    • Journal Title

      Preprint arXiv: quant-ph

      Volume: 2403.20131

    • Related Report
      2023 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Role of the extended Hilbert space in the attainability of the Quantum Cramer-Rao bound for multiparameter estimation2024

    • Author(s)
      Lorcan O. Conlon, Jun Suzuki, Ping Koy Lam, Syed M. Assad
    • Journal Title

      Preprint arXiv: quant-ph

      Volume: 2404.01520

    • Related Report
      2023 Annual Research Report
    • Open Access / Int'l Joint Research
  • [Journal Article] Effect of Wigner rotation on estimating the unitary-shift parameter of a relativistic spin-1/2 particle2022

    • Author(s)
      Shin Funada and Jun Suzuki
    • Journal Title

      physical review A

      Volume: 106 Issue: 6 Pages: 062404-062404

    • DOI

      10.1103/physreva.106.062404

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Presentation] Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem2024

    • Author(s)
      Jun Suzuki
    • Organizer
      Quantum TUT workshop 2024 on quantum statistics and quantum information theory
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tightness of the Nagaoka-Hayashi bound in i.i.d. qubit-state estimation2024

    • Author(s)
      Jianchao Zhang, Jun Suzuki
    • Organizer
      Quantum Information Processing 2024 (qip2024)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical computation of Bayesian Nagaoka-Hayashi bound for three-parameter qubit-state estimationツ?2023

    • Author(s)
      Kehan Zhao, Jun Suzuki
    • Organizer
      第49回量子情報技術研究会(QIT49)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Optimal POVM with minimal size in two-parameter qubit-state estimation2023

    • Author(s)
      Jianchao Zhang, Jun Suzuki
    • Organizer
      第49回量子情報技術研究会(QIT49)
    • Related Report
      2023 Annual Research Report
  • [Presentation] Introduction to Optimal Design of Experiments (DoE) and its Applications to Quantum Estimation2023

    • Author(s)
      Jun Suzuki
    • Organizer
      Quantum Information, Quantum Matter and Quantum Gravity
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Gap Persistence Theorem Between Nagaoka-Hayashi Bound and Holevo Bound for Quantum Multiparameter Estimation2023

    • Author(s)
      Lorcan O. Conlon, Jun Suzuki, Ping Koy Lam, Syed M. Assad
    • Organizer
      IT EMM 合同研究会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 最適な量子測定に基づく量子ニューラルネットワーク分類器の性能特性2022

    • Author(s)
      山田優作, 鈴木淳
    • Organizer
      RCC・ISEC・IT・WBS合同研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] Nagaoka-Hayashi bound in multi-parameter estimation2022

    • Author(s)
      Jun Suzuki
    • Organizer
      Japan-Singapore(NUS) Joint seminar
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Information geometry of the qutrit system based on the Bloch vector representation2022

    • Author(s)
      Yutaro Fukuda, Jun Suzuki
    • Organizer
      Japan-Singapore(NUS) Joint seminar
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Improvement of the performance for quantum neural networks based on optimal quantum measurement2022

    • Author(s)
      Yusaku Yamada, Jun Suzuki
    • Organizer
      Japan-Singapore(NUS) Joint seminar
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] QestOptPOVM: Numerical search for finding an optimal POVM for multiparameter estimation2022

    • Author(s)
      Jianchao Zhang, Jun Suzuki
    • Organizer
      Japan-Singapore(NUS) Joint seminar
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Error trade-off relation for estimating momentum shift of relativistic spin-1/2 particle2022

    • Author(s)
      Shin Funada, Jun Suzuki
    • Organizer
      第47回量子情報技術研究会(QIT47)
    • Related Report
      2022 Research-status Report
  • [Presentation] QestOptPOVM: Numerical search for finding an optimal POVM for multiparameter estimation2022

    • Author(s)
      Jianchao Zhang, Jun Suzuki
    • Organizer
      第47回量子情報技術研究会(QIT47)
    • Related Report
      2022 Research-status Report
  • [Presentation] On Local Attainability of Quantum Cramer-Rao Bound2022

    • Author(s)
      Jun Suzuki
    • Organizer
      第45回情報理論とその応用シンポジウム (SITA2022)
    • Related Report
      2022 Research-status Report
  • [Presentation] Nagaoka-Hayashi bound in multi-parameter estimation2022

    • Author(s)
      Jun Suzuki
    • Organizer
      CQT Seminar, NUS, Singapore
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Introduction to Quantum Information Geometry and its Application to Qutrit system2022

    • Author(s)
      福田優太朗, 鈴木淳
    • Organizer
      芝浦 - 量子基礎論・量子情報オンラインセミナー
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] 量子3準位系における量子Fisher計量の凸結合族のBlochベクトルに基づく解析2022

    • Author(s)
      福田優太朗, 鈴木淳
    • Organizer
      第46回量子情報技術研究会(QIT46)
    • Related Report
      2022 Research-status Report
  • [Presentation] Optimal measurement preserving map for quantum state estimation and hypothesis testing2022

    • Author(s)
      Jun Suzuki
    • Organizer
      IT EMM 合同研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] Effect of Wigner rotation on estimating momentum shift of relativistic spin-1/2 particle2021

    • Author(s)
      Shin Funada, Jun Suzuki
    • Organizer
      The 45th Quantum Information Technology Symposium
    • Related Report
      2021 Research-status Report
  • [Presentation] Quantum Information Geometry of Weakly Contaminated Models2021

    • Author(s)
      Jun Suzuki
    • Organizer
      The 44th Symposium on Information Theory and its Applications
    • Related Report
      2021 Research-status Report
  • [Presentation] Bayesian Holevo and Nagaoka-Hayashi bounds for quantum-state estimation2021

    • Author(s)
      Jun Suzuki
    • Organizer
      電子情報通信学会,情報理論研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Effect of Wigner rotation on estimating momentum shift of relativistic spin-1/2 particle2021

    • Author(s)
      Shin Funada, Jun Suzuki
    • Organizer
      25th Annual Conference on Quantum Information Processing
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research

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Published: 2021-04-28   Modified: 2025-01-30  

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