π -Corrected Heisenberg Limit

Wojciech Gorecki, Rafał Demkowicz-Dobrzański, Howard M. Wiseman, Dominic W. Berry

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    28 Citations (Scopus)
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    Abstract

    We consider the precision Δφ with which the parameter φ, appearing in the unitary map Uφ=eiφΛ, acting on some type of probe system, can be estimated when there is a finite amount of prior information about φ. We show that, if Uφ acts n times in total, then, asymptotically in n, there is a tight lower bound Δφ≥π/[n(λ+-)], where λ+, λ- are the extreme eigenvalues of the generator Λ. This is greater by a factor of π than the conventional Heisenberg limit, derived from the properties of the quantum Fisher information. That is, the conventional bound is never saturable. Our result makes no assumptions on the measurement protocol and is relevant not only in the noiseless case but also if noise can be eliminated using quantum error correction techniques.

    Original languageEnglish
    Article number030501
    Pages (from-to)030501-1-030501-5
    Number of pages5
    JournalPhysical Review Letters
    Volume124
    Issue number3
    DOIs
    Publication statusPublished - 23 Jan 2020

    Bibliographical note

    Copyright 2020 American Physical Society. Firstly published in Physical Review Letters, 124(3), 030501. The original publication is available at https://doi.org/10.1103/PhysRevLett.124.030501. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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