Uselessness of sub-Heisenberg estimation strategies

Details Uselessness of sub-Heisenberg estimation strategies Uselessness of sub-Heisenberg estimation strategies

2012-01-09

arxiv.org/abs/1201.1878v1

Physics

Quantum Physics

4 pages, 2 figures

Scientific paper

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 they are basically useless: 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, and 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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