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個人情報保護と推定精度のトレードオフ関係及びそれに関連した量子効果の数学的解析

Research Project

Project/Area Number 19J20161
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionNagoya University

Principal Investigator

吉田 裕哉  名古屋大学, 多元数理科学研究科, 特別研究員(PD)

Project Period (FY) 2019-04-25 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2021: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2020: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2019: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords最適化 / 量子状態 / 差分プライバシー / 状態識別 / 一般確率論 / capacity / product basis / 漸近的decoupling / mixing
Outline of Research at the Start

個人情報を集め, そこから必要な統計量を推定することがしばしば行われる. その際, 個人情報を保護しつつ推定精度を高めることは当然の要求である. しかし, 個人情報保護と推定精度はトレードオフ関係にある. 本研究では, このトレードオフ関係の最適化を目的とする. こうしたトレードオフ関係の最適化は, これまで古典情報を用いて研究されてきた. しかし, 本研究では量子状態を用いたトレードオフ関係の最適化も考える. さらに, 上記トレードオフ関係に関連して, 通信路や不確定性関係に関する研究も行う.

Outline of Annual Research Achievements

2021年度は, 2020年度までの研究に足りなかった数学的な解析を行った. 以下, 2020年度の研究と比較しつつ, 2021年度の研究について述べる.
古典的データXを量子状態に変換した際の差分プライバシーを古典量子DP, Xを別の古典的データに変換した際の差分プライバシーを古典DPと記す. 差分プライバシーでは, 正のパラメータεでプライバシーレベルを表す. たとえば, εが小さいとプライバシーレベルが高く, εが大きいとプライバシーレベルが低い. 2020年度までの研究では, 同じプライバシーレベル (同じε) の場合に古典と量子を比較した.
2021年度は, 異なるプライバシーレベル (異なるε) の場合に古典と量子を比較し, 古典DPと古典量子DPの差をプライバシーレベルのずれで定量的に評価することに成功した. これをもう少し詳しく述べる. ここで注目したい性質は, 有用性 (utility) とプライバシーレベルである. 一般に, プライバシーレベルを下げれば有用性が上がり, プライバシーレベルを上げれば有用性が下がる. これを踏まえると, 2021年度の研究成果は以下である. 一般に, 有用性は古典DPより古典量子DPの方が優れている (2020年度までの研究). しかし, 古典のプライバシーレベルを犠牲にすれば, 有用性の関係が逆転することを示した. さらに, どの程度プライバシーレベルを犠牲にすれば有用性の関係が逆転するのか, 定量的に評価した.

Research Progress Status

令和3年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和3年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • Research Products

    (33 results)

All 2022 2021 2020 2019

All Journal Article (6 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 6 results,  Open Access: 3 results) Presentation (27 results) (of which Int'l Joint Research: 13 results,  Invited: 1 results)

  • [Journal Article] Maximum dimension of subspaces with no product basis2021

    • Author(s)
      Yuuya Yoshida
    • Journal Title

      Linear Algebra and its Applications

      Volume: 620 Pages: 228-241

    • DOI

      10.1016/j.laa.2021.03.001

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Distributions of finite sequences represented by polynomials in Piatetski-Shapiro sequences2021

    • Author(s)
      Kota Saito and Yuuya Yoshida
    • Journal Title

      Journal of Number Theory

      Volume: 222 Pages: 115-156

    • DOI

      10.1016/j.jnt.2020.12.004

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perfect discrimination in approximate quantum theory of general probabilistic theories2020

    • Author(s)
      Yuuya Yoshida, Hayato Arai and Masahito Hayashi
    • Journal Title

      Physical Review Letters

      Volume: 125 Issue: 15 Pages: 150402-150402

    • DOI

      10.1103/physrevlett.125.150402

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Classical mechanism is optimal in classical-quantum differentially private mechanisms2020

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Journal Title

      Proceedings of 2020 IEEE International Symposium on Information Theory

      Volume: - Pages: 1973-1977

    • DOI

      10.1109/isit44484.2020.9174484

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Asymptotic properties for Markovian dynamics in quantum theory and general probabilistic theories2020

    • Author(s)
      Y. Yoshida and M. Hayashi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: - Issue: 21 Pages: 215303-215303

    • DOI

      10.1088/1751-8121/ab8599

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory2019

    • Author(s)
      H. Arai, Y. Yoshida, and M. Hayashi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 52 Issue: 46 Pages: 465304-465304

    • DOI

      10.1088/1751-8121/ab4b64

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 古典量子差分プライバシーの数学的側面2022

    • Author(s)
      吉田 裕哉
    • Organizer
      第5回数理新人セミナー
    • Related Report
      2021 Annual Research Report
  • [Presentation] 古典量子差分プライバシーの数学的側面2022

    • Author(s)
      吉田 裕哉
    • Organizer
      第18回数学総合若手研究集会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 古典量子差分プライバシーの数学的側面2021

    • Author(s)
      吉田 裕哉
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 局所差分プライバシー下での最適化における古典と量子の比較2021

    • Author(s)
      吉田 裕哉
    • Organizer
      大規模データの公開におけるプライバシー保護の理論と応用
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Perfect discrimination in approximate quantum theory of general probabilistic theories2021

    • Author(s)
      Yuuya Yoshida, Hayato Arai and Masahito Hayashi
    • Organizer
      24th Annual Conference on Quantum Information Processing
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Product basisを持たない部分空間の最大次元2021

    • Author(s)
      吉田 裕哉
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 多項式で表せる有限列の分布とHardy field2021

    • Author(s)
      齋藤 耕太, 吉田 裕哉
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Product basisを持たない部分空間の最大次元2021

    • Author(s)
      吉田 裕哉
    • Organizer
      第17回数学総合若手研究集会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Perfect discrimination in approximate quantum theory of general probabilistic theories2020

    • Author(s)
      Yuuya Yoshida, Hayato Arai and Masahito Hayashi
    • Organizer
      20th Asian Quantum Information Science Conference
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Perfect discrimination in approximate quantum theory of general probabilistic theories2020

    • Author(s)
      吉田 裕哉, 荒井 駿, 林 正人
    • Organizer
      第43回量子情報技術研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 多項式で表せる有限列の分布とHardy field2020

    • Author(s)
      吉田 裕哉
    • Organizer
      解析的整数論の展望と諸問題
    • Related Report
      2020 Annual Research Report
  • [Presentation] Classical mechanism is optimal in classical-quantum differentially private mechanisms2020

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      2020 IEEE International Symposium on Information Theory
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory2020

    • Author(s)
      Hayato Arai, Yuuya Yoshida and Masahito Hayashi
    • Organizer
      23rd Annual Conference on Quantum Information Processing
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Necessary and sufficient condition of asymptotic decoupling for Markovian quantum dynamics2020

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      23rd Annual Conference on Quantum Information Processing
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Piatetski-Shapiro列に含まれる等差数列の分布2020

    • Author(s)
      吉田 裕哉
    • Organizer
      第25回代数学若手研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 対称錐と状態識別 一般確率論の観点から2020

    • Author(s)
      吉田 裕哉
    • Organizer
      第3回数理新人セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory2019

    • Author(s)
      Hayato Arai, Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Beyond i.i.d. in Information Theory
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic properties for quantum dynamics2019

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Beyond i.i.d. in Information Theory
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory2019

    • Author(s)
      Hayato Arai, Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Nagoya-SUSTech Quantum Information Workshop
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic properties for quantum dynamics2019

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Nagoya-SUSTech Quantum Information Workshop
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory2019

    • Author(s)
      Hayato Arai, Yuuya Yoshida and Masahito Hayashi
    • Organizer
      19th Asian Quantum Information Science Conference
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Necessary and sufficient condition of asymptotic decoupling for Markovian quantum dynamics2019

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      19th Asian Quantum Information Science Conference
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Perfect discrimination of non-orthogonal separable pure states on bipartite system in general probabilistic theory2019

    • Author(s)
      Hayato Arai, Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Quantum Information Processing in Non-Markovian Quantum Complex Systems
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Necessary and sufficient condition of asymptotic decoupling for Markovian quantum dynamics2019

    • Author(s)
      Yuuya Yoshida and Masahito Hayashi
    • Organizer
      Quantum Information Processing in Non-Markovian Quantum Complex Systems
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2部量子系におけるseparable状態の完全識別 一般確率論の観点から2019

    • Author(s)
      荒井 駿, 吉田 裕哉, 林 正人
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 一般確率論における非直交separable状態の完全識別2019

    • Author(s)
      荒井 駿, 吉田 裕哉, 林 正人
    • Organizer
      第40回量子情報技術研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 量子dynamicsにおける漸近的decouplingの必要十分条件2019

    • Author(s)
      吉田 裕哉, 林 正人
    • Organizer
      第40回量子情報技術研究会
    • Related Report
      2019 Annual Research Report

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Published: 2019-05-29   Modified: 2024-03-26  

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