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Statistical Inference of Quantum Measurements

Research Project

Project/Area Number 20K03774
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionToyohashi University of Technology (2023)
Kyoto University (2020-2022)

Principal Investigator

DALLARNO Michele  豊橋技術科学大学, 工学(系)研究科(研究院), 准教授 (50870052)

Project Period (FY) 2020-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsstatistical inference / quantum measurements / 2 designs / testing regions / Lorenz curve / conical approximations / John ellipsoid / data-driven inference / quantum inference / quantum measurement / quantum design / quantum devices / machine learning / regular simplices / SIC measurements
Outline of Research at the Start

This research plan will produce analytical and numerical results on the relevant problem of the statistical inference of quantum measurements. It will also produce implementations of quantum algorithms for the machine learning of quantum measurement with the IBM Q quantum computer.

Outline of Annual Research Achievements

In the FY2023, I generalized my previous results on the statistical inference of quantum measurements, that were restricted to the qubit case, to the arbitrary dimensional case. This could be achieved by first characterizing inner and outer conical approximations of the range of arbitrary dimensional quantum measurements. Such approximations are tight, that is, they are maximal and minimal in volume among all conical approximatins, and are close, that is, the one is transformed into the other by a constant rescaling. I showed that any measurement that produces a given set of conditional probability distributions upon the input of a 2-design set of states, maximizes the Bayesian posterior probability distribution in the inferential process. I also showed how to apply the aforementioned results to the device independent testing of the statistical sufficiency of quantum measurements. I presented my results in 21 presentations, including keynote and invited speeches in international conferences including the Analytical and Combinatorial Methods in Quantum Information Thoery II (Edinburgh, UK, July 2023), Quantum Foundation workshop (Graz, Austria, August 2023), and ICAICTA (Lonbok, Indonesia, October 2023).

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

The project is progressing smoothly. Several papers have been published by me and collaborators on the topic.

M. Dall'Arno, F. Buscemi, T. Koshiba, Computing the quantum guesswork: a quadratic assignment problem, QIC 23, 0721 (2023); M. Dall'Arno, On the Measurement attaining the Quantum Guesswork, IEEE Trans. Inform. Theory 70, 2713 (2024); B. Avirmed, K. Niinomi, M. Dall'Arno, Adversarial guesswork with quantum side information, QIC 23, 1105 (2023)

M. Dall'Arno, On the role of designs in the data-driven approach to quantum statistical inference, arXiv:2304.13258; M. Dall'Arno, F. Buscemi, Tight conic approximation of testing regions for quantum statistical models and measurements, arXiv:2309.16153; M. Dall'Arno, A. Tosini, F. Buscemi, The signaling dimension in generalized probabilistic theories, arXiv:2311.13103

Strategy for Future Research Activity

The natural development of the present research project is in the device-independent approach to quantum resource theories. On the one hand, the device-independent approach to Quantum Theory dictates that experimental results should be interpreted without any assumption on the devices involved, and accordingly allows for the theory itself to be tested. On the other hand, the resource-theoretical approach to Quantum Theory is based on establishing a hierarchy among devices based on the ability of some devices to simulate other devices. I plan to extend and unify these two approaches, that so far have separately drawn a considerable interest by two distinct communities. To this aim, I will overcome many of the limitations of the state of the art in each field, in particular by
extending known results beyond the binary and two-dimensional case. As a result, I will
show how to certify, in a device-independent way, whether any given quantum device is
able of simulating any other given device, thus establishing a device-independent
hierarchy among devices based on the simulability criterion.

Report

(4 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (39 results)

All 2024 2023 2022 2021 2020 Other

All Journal Article (9 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 5 results,  Open Access: 4 results) Presentation (27 results) (of which Int'l Joint Research: 13 results,  Invited: 11 results) Remarks (1 results) Funded Workshop (2 results)

  • [Journal Article] On the Measurement Attaining the Quantum Guesswork2024

    • Author(s)
      Dall’Arno Michele
    • Journal Title

      IEEE Transactions on Information Theory

      Volume: 70 Issue: 4 Pages: 2713-2719

    • DOI

      10.1109/tit.2023.3343676

    • Related Report
      2023 Research-status Report
  • [Journal Article] Adversarial guesswork with quantum side information2023

    • Author(s)
      Avirmed Baasanchimed、Niinomi Kaito、Dall'Arno Michele
    • Journal Title

      Quantum Information and Computation

      Volume: 23 Issue: 13&14 Pages: 1105-1118

    • DOI

      10.26421/qic23.13-14-3

    • Related Report
      2023 Research-status Report
  • [Journal Article] Computing the quantum guesswork: a quadratic assignment problem2023

    • Author(s)
      Dall'Arno, M; Buscemi, F; Koshiba, T
    • Journal Title

      Quantum Information and Computation

      Volume: 23 Issue: 9&10 Pages: 721-732

    • DOI

      10.26421/qic23.9-10-1

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The signaling dimension of physical systems2022

    • Author(s)
      Dall'Arno Michele
    • Journal Title

      Quantum Views

      Volume: 6 Pages: 66-66

    • DOI

      10.22331/qv-2022-08-25-66

    • Related Report
      2022 Research-status Report
  • [Journal Article] Guesswork of a Quantum Ensemble2022

    • Author(s)
      Dall'Arno Michele、Buscemi Francesco、Koshiba Takeshi
    • Journal Title

      IEEE Transactions on Information Theory

      Volume: 68 Issue: 5 Pages: 3139-3143

    • DOI

      10.1109/tit.2022.3146463

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Worst-case Quantum Hypothesis Testing with Separable Measurements2020

    • Author(s)
      Le Phuc Thinh, Michele Dall'Arno, Valerio Scarani
    • Journal Title

      Quantum 4

      Volume: 4 Pages: 320-320

    • DOI

      10.22331/q-2020-09-11-320

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Data-driven inference, reconstruction, and observational completeness of quantum devices2020

    • Author(s)
      Dall'Arno Michele、Buscemi Francesco、Bisio Alessandro、Tosini Alessandro
    • Journal Title

      Physical Review A

      Volume: 102 Issue: 6 Pages: 062407-062407

    • DOI

      10.1103/physreva.102.062407

    • NAID

      120007145960

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Explicit construction of optimal witnesses for input--output correlations attainable by quantum channels2020

    • Author(s)
      Michele Dall'Arno, Sarah Brandsen, Francesco Buscemi
    • Journal Title

      In print, Open Systems & Information Dynamics

      Volume: 27

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Guesswork of a quantum ensemble2020

    • Author(s)
      Michele Dall'Arno, Francesco Buscemi, Takeshi Koshiba
    • Journal Title

      arXiv:2012.09350

      Volume: N.A.

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Presentation] Tradeoff relations between entropic quantities and their application in quantum information theory2024

    • Author(s)
      Michele Dall'Arno
    • Organizer
      IEICE IT meeting
    • Related Report
      2023 Research-status Report
  • [Presentation] The signaling dimension and the no-hypersignaling principle2024

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Foundations
    • Related Report
      2023 Research-status Report
  • [Presentation] The quantum decoding attaining the minimum guesswork with single-qubit side information2024

    • Author(s)
      Michele Dall'Arno
    • Organizer
      IEICE IT meeting
    • Related Report
      2023 Research-status Report
  • [Presentation] Guesswork of quantum ensembles2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Memorial Workshop for Takeshi Koshiba
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] Quantum testing regions and the generalized Alberti-Ulhmann criterion2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information Technology (QIT) 49
    • Related Report
      2023 Research-status Report
  • [Presentation] The computation of the signaling dimension2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information Technology (QIT) 49
    • Related Report
      2023 Research-status Report
  • [Presentation] Tight conic approximation of testing regions for quantum statistical models and measurements2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Nagoya-KAIST workshop
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tight conic approximation of testing regions for quantum statistical models and measurements2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Recent Advances in Quantum Mathematical Statistics
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal classical simulation of physical systems2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Simulations and Quantum Walks
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] A device-independent approach to quantum simulability2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Simulations and Quantum Walks
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Bayesian Inference of quantum devices2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      ICAICTA
    • Related Report
      2023 Research-status Report
  • [Presentation] On the role of designs in the data-driven approach to quantum statistical inference2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information, Quantum Matter and Quantum Gravity
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum Guesswork: a combinatorial instance of quantum hypothesis testing2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information, Quantum Matter and Quantum Gravity
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantum Verification2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      NTT
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] Quantum Guesswork2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Graz University of Technology
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Role of SIC Structures in the Quantum Inferential Process2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      The Quantum Reconstruction Program and Beyond
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Bayesian Inference of Quantum Devices2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Pavia University, Italy
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum guesswork: a combinatorial instance of quantum hypothesis testing2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Analytical and Combinatorial Methods in Quantum Information Theory II
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum Guesswork2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Pavia University
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum guesswork -- A combinatorial instance of quantum hypothesis testing2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information Technology (QIT) 48
    • Related Report
      2023 Research-status Report
  • [Presentation] Data-driven quantum inference -- An application of statistical inference to the self-calibration of quantum devices2023

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information Technology (QIT) 48
    • Related Report
      2023 Research-status Report
  • [Presentation] Guesswork of quantum ensembles2022

    • Author(s)
      Michele Dall'Arno
    • Organizer
      13th KCIK-ICTQT Symposium on Quantum Information
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimally-committal quantum measurements2022

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Third Kyoto Workshop on Quantum Information, Computation, and Foundations
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Classical information storage in an n-level quantum system2022

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Nagoya University
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Guesswork of a quantum ensemble2022

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Second Kyoto Workshop on Quantum Information, Computation, and Foundation
    • Related Report
      2021 Research-status Report
  • [Presentation] Bootstrapping quantum tomography by data-driven inference2021

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information Processing
    • Related Report
      2020 Research-status Report
  • [Presentation] Data-driven inference of quantum devices2020

    • Author(s)
      Michele Dall'Arno
    • Organizer
      Quantum Information, Computation, and Foundations
    • Related Report
      2020 Research-status Report
  • [Remarks] Quantum Information group in TUT

    • URL

      https://micheledallarno.wordpress.com/

    • Related Report
      2023 Research-status Report
  • [Funded Workshop] Quantum Toyohashi international workshop on quantum information and quantum statistics2024

    • Related Report
      2023 Research-status Report
  • [Funded Workshop] Third Kyoto Workshop on Quantum Information, Computation, and Foundations2022

    • Related Report
      2022 Research-status Report

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Published: 2020-04-28   Modified: 2024-12-25  

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