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.\

}, doi = {10.1088/1367-2630/18/10/103049}, url = {http://stacks.iop.org/1367-2630/18/i=10/a=103049?key=crossref.fb78efa5084e8d9fdb51f574cf3bfed3http://stacks.iop.org/1367-2630/18/i=10/a=103049/pdfhttp://stacks.iop.org/1367-2630/18/i=10/a=103049?key=crossref.fb78efa5084e8d9fdb51f574cf3bfed3}, author = {Calsamiglia, J and Gendra, B and Mu{\~n}oz-Tapia, R and Bagan, E} }