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The conventional formulation of quantum sensing is based on the assumptionthat the probe is reset to its initial state after each measurement. In a verydistinct approach, one can also pursue a sequential measurement scheme in whichtime-consuming resetting is avoided. In this situation, every measurementoutcome effectively comes from a different probe, yet correlated with otherdata samples. Finding a proper description for the precision of sequentialmeasurement sensing is very challenging as it requires the analysis of longsequences with exponentially large outcomes. Here, we develop a recursiveformula and an efficient Monte-Carlo approach to calculate the Fisherinformation, as a figure of merit for sensing precision, for arbitrary lengthsof sequential measurements. Our results show that Fisher information initiallyscales non-linearly with the number of measurements and then asymptoticallysaturates to linear scaling. Such transition, which fundamentally constrainsthe extractable information about the parameter of interest, is directly linkedto the finite memory of the probe when undergoes multiple sequentialmeasurements. Based on these, we establish a figure of merit to determine theoptimal measurement sequence length and exemplify our results in threedifferent physical systems.

Extractable Information Capacity in Sequential Measurements Metrology