Extractable Information Capacity in Sequential Measurements Metrology

TL;DR

This paper develops a recursive and Monte-Carlo method to analyze the Fisher information in sequential quantum measurements without resetting probes, revealing a transition from nonlinear to linear information scaling due to finite memory effects.

Contribution

It introduces a novel recursive formula and efficient Monte-Carlo approach to quantify sensing precision in sequential measurements, accounting for finite probe memory effects.

Findings

Fisher information scales non-linearly initially and then linearly with measurements

Finite probe memory causes a transition in information scaling

Method applied to three different physical systems

Abstract

The conventional formulation of quantum sensing is based on the assumption that the probe is reset to its initial state after each measurement. In a very distinct approach, one can also pursue a sequential measurement scheme in which time-consuming resetting is avoided. In this situation, every measurement outcome effectively comes from a different probe, yet correlated with other data samples. Finding a proper description for the precision of sequential measurement sensing is very challenging as it requires the analysis of long sequences with exponentially large outcomes. Here, we develop a recursive formula and an efficient Monte-Carlo approach to calculate the Fisher information, as a figure of merit for sensing precision, for arbitrary lengths of sequential measurements. Our results show that Fisher information initially scales non-linearly with the number of measurements and then asymptotically saturates to linear scaling. Such transition, which fundamentally constrains the extractable information about the parameter of interest, is directly linked to the finite memory of the probe when undergoes multiple sequential measurements. Based on these, we establish a figure of merit to determine the optimal measurement sequence length and exemplify our results in three different physical systems.