Tight bounds on the simultaneous estimation of incompatible parameters

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Sidhu, Jasminder S. and Ouyang, Yingkai and Campbell, Earl T. and Kok, Pieter (2020) Tight bounds on the simultaneous estimation of incompatible parameters. Preprint / Working Paper. arXiv.org, Ithaca, New York.

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Abstract

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has greatly diminished the applicability of estimation theory in many practical implementations. The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimisation over multiple variables. In this work, we show that the HCRB can be solved analytically for two parameters. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations. We apply our formalism to magnetic field sensing. Our results provide fundamental insight and make significant progress towards the estimation of multiple incompatible observables.

ORCID iDs

Sidhu, Jasminder S. ORCID logoORCID: https://orcid.org/0000-0002-6167-8224, Ouyang, Yingkai, Campbell, Earl T. and Kok, Pieter;
  • Item type:Monograph(Preprint / Working Paper)
    ID code:74122
    Dates:
    Date
    Event
    6 August 2020
    Published
    19 December 2019
    Submitted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:07 Oct 2020 13:47
    Last modified:16 Dec 2024 01:18
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/74122
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