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Inspired by the notion that environmental noise is in principle observable,whilst fundamental noise due to spontaneous localisation would not be, we studythe estimation of the diffusion parameter induced by wave function collapsemodels under continuous monitoring of the environment. We take into accountfinite measurement efficiencies and, in order to quantify the advantage grantedby monitoring, we analyse the quantum Fisher information associated with such adiffusion parameter, identify optimal measurements in limiting cases, andassess the performance of such measurements in more realistic conditions.

Unravelling the noise: the discrimination of wave function collapse models under time-continuous measurements