Abstract Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.

中文翻译：

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多参数估计中贝叶斯边界的实验研究

摘要 量子参数估计为具有量子优势的传感器设计提供了坚实的概念基础。这不仅通过支持和利用量子特性的硬件来实现，而且数据分析也有其影响和相关性。在这方面，贝叶斯方法已经成为一种有效而优雅的解决方案，其好处是自然地结合了先验信息的可用性。在本文中，我们提出了对多相位估计的贝叶斯方法的评估，该评估基于超出参数估计中假设的大样本通常限制的范围进行评估。重要的是，这些方法适用于由单光子播种的三臂干涉仪的输出统计数据生成的实验数据。