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  • Does Nonlinear Metrology Offer Improved Resolution? Answers from Quantum Information Theory

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    Author(s)
    Hall, Michael JW
    Wiseman, Howard M
    Griffith University Author(s)
    Wiseman, Howard M.
    Year published
    2012
    Metadata
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    Abstract
    A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the mean photon number of the probe state. These suggestions are based on calculations of "local precision" for particular nonlinear schemes. However, we show that there is no simple connection between the local precision and the average estimation error for these schemes, leading to a scaling puzzle. This puzzle is partially resolved by a careful analysis of iterative implementations of the ...
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    A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the mean photon number of the probe state. These suggestions are based on calculations of "local precision" for particular nonlinear schemes. However, we show that there is no simple connection between the local precision and the average estimation error for these schemes, leading to a scaling puzzle. This puzzle is partially resolved by a careful analysis of iterative implementations of the suggested nonlinear schemes. However, it is shown that the suggested nonlinear schemes are still limited to an exponential scaling in vn. (This scaling may be compared to the exponential scaling in n which is achievable if multiple passes are allowed, even for linear schemes.) The question of whether nonlinear schemes may have a scaling advantage in the presence of loss is left open. Our results are based on a new bound for average estimation error that depends on (i) an entropic measure of the degree to which the probe state can encode a reference phase value, called the G asymmetry, and (ii) any prior information about the phase shift. This bound is asymptotically stronger than bounds based on the variance of the phase-shift generator. The G asymmetry is also shown to directly bound the average information gained per estimate. Our results hold for any prior distribution of the shift parameter, and generalize to estimates of any shift generated by an operator with discrete eigenvalues.
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    Journal Title
    Physical Review X
    Volume
    2
    Issue
    4
    DOI
    https://doi.org/10.1103/PhysRevX.2.041006
    Copyright Statement
    © The Author(s) 2012. For information about this journal please refer to the publisher’s website or contact the authors. Articles are licensed under the terms of the Creative Commons Attribution 3.0 Unported License (http://creativecommons.org/licenses/by/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, providing that the work is properly cited.
    Subject
    Condensed matter physics
    Quantum physics
    Degenerate quantum gases and atom optics
    Quantum information, computation and communication
    Quantum optics and quantum optomechanics
    Publication URI
    http://hdl.handle.net/10072/48614
    Collection
    • Journal articles

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