Probabilistic metrology or how some measurement outcomes render ultra-precise estimates

Abstract

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision that exceeds the deterministic bounds for the average precision. This establishes a new ultimate bound on the phase estimation precision of particular measurement outcomes (or sequence of outcomes). For probe systems subject to local dephasing, we quantify such precision limit as a function of the probability of failure that can be tolerated. Our results show that the possibility of abstaining can set back the detrimental effects of noise.

arXiv commentImproved version of arXiv:1407.6910 with an extended introduction where we clarify our approach to metrology, and probabilistic metrology in particular. Changed title

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