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.

中文翻译：

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贝叶斯量子估计基准测试


追求参数估计的精度是不同科学领域的一项基本任务。因此，这个问题的相关性提供了开发将量子资源应用于估计协议的方法的动力。在此背景下，贝叶斯估计为最佳量子计量技术（例如自适应协议）提供了完整的框架。然而，使用贝叶斯方法需要大量的计算资源，特别是在代表量子传感器典型操作场景的多参数估计中。因此，描述实施贝叶斯估计的协议的要求可能成为一个重大挑战。这项工作的重点是在单参数和多参数场景中对这些协议的性能进行稳健的基准测试。通过比较不同的品质因数，提供了有利于在估计中使用二次误差中值的证据，以减轻由于参数空间的数值离散、有限数据的存在和数值不稳定性造成的杂散效应。这些结果提供了贝叶斯协议的稳健且可靠的表征，在量子估计框架内找到了实际问题的自然应用。