Benchmarking Bayesian quantum estimation
arXiv:2401.14900 · doi:10.1088/2058-9565/ad48b3
Abstract
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
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- Exponentially-enhanced quantum sensing with many-body phase transitions
- Metrological symmetries in singular quantum multi-parameter estimation
- Saturable global quantum sensing
- On the role of symmetry and geometry in global quantum sensing
- Adaptive, symmetry-informed Bayesian metrology for precise quantum technology measurements