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We consider the impact that temporal correlations in the measurementstatistics can have on the achievable precision in a sequential metrologicalprotocol. In this setting, and for a single quantum probe, we establish that itis the transitions between the measurement basis states that plays the mostsignificant role in determining the precision, with the resulting conditionalFisher information being interpretable as a rate of information acquisition.Projective measurements are shown to elegantly demonstrate this in twodisparate estimation settings. Firstly, in determining the temperature of anenvironment and, secondly, to ascertain a parameter of the system Hamiltonian.In both settings we show that the sequential estimation approach can provide auseful method to enhance the achievable precision.

Fisher information rates in sequentially measured quantum systems