Bayesian estimation of one-parameter qubit gates

TL;DR

This paper investigates optimal Bayesian methods for estimating one-parameter qubit gates, analyzing probe strategies, measurement stability, and the benefits of entanglement to enhance precision and robustness.

Contribution

It provides a detailed analysis of Bayesian estimation techniques for qubit gates, including the use of entanglement and stability considerations, advancing quantum gate characterization methods.

Findings

Bayesian estimators approach quantum limits after limited runs

Entanglement improves estimation stability

Asymptotic optimality is achievable with few measurements

Abstract

We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure. Bayesian inference is employed and compared with the ultimate quantum limits to precision, taking into account the biased nature of Bayes estimator in the non asymptotic regime. Besides, through the evaluation of the asymptotic a posteriori distribution for the gate parameter and the comparison with the results of Monte Carlo simulated experiments, we show that asymptotic optimality of Bayes estimator is actually achieved after a limited number of runs. The robustness of the estimation procedure against fluctuations of the measurement settings is investigated and the use of entanglement to improve the overall stability of the estimation scheme is also analyzed in some details.