Bayesian multiparameter quantum metrology with limited data

Abstract

A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios, which typically involve multiple parameters, limited measurement data and some degree of prior information. Here we present a practical strategy for achieving just this. First we derive a new Bayesian multi-parameter quantum bound. We then show how to construct the optimal measurement when our bound can be saturated for a single shot and consider experiments involving a repeated sequence of these measurements. Our method properly accounts for the number of measurements and the degree of prior information, and we illustrate our ideas with a qubit sensing network and a model for phase imaging. This approach provides a powerful and useful technique for implementing quantum metrology in a wide-range of practical scenarios as well as gaining new insights about the role of local and global strategies.

Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation

“…More rigorous analysis beyond the framework of the quantum Cramér-Rao bound is necessary to see whether or not the states discussed in this work can beat at least the weak Heisenberg limit for practical purposes [17,18]. We leave similar investigation for unbounded photon number distributions as a future study.…”

“…This implies that the probe state with the maximal photon number variance would possibly be the theoretical optimal state for single-mode phase estimation. Here, we aim to introduce, while leaving the proof of the achievability of the quantum Cramér-Rao bound to future studies [17,18], fiducial quantum states that have the maximum, or at least a larger photon number variance than that available with the squeezed vacuum state-the paradigmatic state known to be useful for quantum phase estimation. We distinguish the scenarios when the photon number probability distribution is either bounded or unbounded, i.e., defined within a finite or an infinite domain [19].…”

“…That is, fortunately, often the case, e.g., for plasmonic sensors [36,37] or phase tracking [38]. In such cases, the validity of the quantum Cramér-Rao bound can be investigated in terms of the required minimum number of measurements and the minimum prior knowledge of the parameter [17,18].…”

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

“…In these instances, adaptive protocols are useful to achieve optimality, as already accomplished for single parameter estimation [190][191][192]. Recent theoretical investigations suggest this may also be the case when addressing the multiparameter case [193].…”

Adaptive phase estimation through a genetic algorithm

“…Even the study of photonic realization of probes states can be improved by GA algorithms [47,50,51], giving rise to accessible and robust-to-noise states for metrology tasks. Then, a natural generalization of this approach is to apply GA optimization for offline protocols in multiparameter quantum metrology problems [17,[77][78][79], with particular attention to the limited data regime [80]. While online adaptive Bayesian techniques for multiphase estimation were demonstrated [81], offline solutions have still to be explored and GA promises to be a useful tool for this task.…”