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Probabilistic metrology defeats ultimate deterministic bound

Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and biosensing. Quantum metrology studies the fundamental limits in the estimation precision given a certain amount of resources (e.g. the number of probe systems) and restrictions (e.g. limited interaction time, or coping with unavoidable presence of noise). Here we show 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 violates the deterministic bounds. This establishes a new ultimate quantum metrology limit. For probe systems subject to local dephasing, we quantify such precision limit as a function of the probability of failure that can be tolerated. We show that the possibility of abstaining can substantially set back the detrimental effects of noise.