Probabilistic metrology or how some measurement outcomes render   ultra-precise estimates
  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. 
J. Calsamiglia, B. Gendra, R. Munoz-Tapia, and E. Bagan
quant-ph