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arXiv · 1201.1878

Sub-Heisenberg estimation strategies are ineffective

Vittorio Giovannetti·Lorenzo Maccone
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Abstract

In interferometry, sub-Heisenberg strategies claim to achieve a phase estimation error smaller than the inverse of the mean number of photons employed (Heisenberg bound). Here we show that one can achieve a comparable precision without performing any measurement, just using the large prior information that sub-Heisenberg strategies require. For uniform prior (i.e. no prior information), we prove that these strategies cannot achieve more than a fixed gain of about 1.73 over Heisenberg-limited interferometry. Analogous results hold for arbitrary single-mode prior distributions. These results extend also beyond interferometry: the effective error in estimating any parameter is lower bounded by a quantity proportional to the inverse expectation value (above a ground state) of the generator of translations of the parameter.

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Vittorio Giovannetti, Lorenzo Maccone. 2012-01-09. Sub-Heisenberg estimation strategies are ineffective. https://doi.org/10.1103/physrevlett.108.210404

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