Optimal precision of parameter estimation in images with local sub-Poissonian quantum fluctuations |
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Authors: | J Fade N Treps C Fabre P Réfrégier |
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Institution: | 1.Physics and Image Processing Group, Institut Fresnel, Aix-Marseille Université, école Centrale Marseille, CNRS,Marseille,France;2.Quantum Optics Group, Laboratoire Kastler Brossel, Université Pierre et Marie Curie-Paris 6, école Normale Supérieure, CNRS,Paris Cedex 05,France |
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Abstract: | Non-classical quantum effects allow light with local
sub-Poissonian fluctuations below shot noise to be produced. We show
that using such light can improve the estimation precision of a
parameter in an image beyond the standard Poissonian limit. This
benefit is theoretically investigated by means of a phenomenological
model of local sub-Poissonian noise which assumes the independence
of the fluctuations in each pixel. In particular, a bound on the
best precision expectable independently of the exact unbiased
estimation protocol used, which is given by the Cramer-Rao bound, is
determined from this model. The numerical simulations presented in
the special case of the estimation of a displacement of an image
perturbed with local sub-Poissonian noise show that a standard
estimator can overcome the classical Poissonian limit by reaching
this limit precision only beyond a certain value of the photon flux
which we characterize. We eventually present some numerical results
that demonstrate the generality of the model proposed, of the
optimality bounds and of the estimator performance. |
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Keywords: | |
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