title: Sub-Heisenberg estimation strategies are ineffective.
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.
authors.affiliation: NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Pisa, Italy.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Giovannetti
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Maccone