Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramr–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

贝叶斯分析是一种参数估计的框架，即使在不确定性条件下，该条件也无法适用，在不确定性条件下，基于Cramr-Rao界线（CRB）的常用局部（频率）分析没有得到很好的定义。特别地，当没有关于参数值的初始信息可用时，例如，当执行很少的测量时，它适用。在这里，我们考虑连续变量（CV）量子计量学中的三种范式估计方案（位移，相位和挤压强度的估计），并从贝叶斯角度分析它们。对于每种情况，我们研究在零差和外差检测下使用单模高斯态可获得的精度。这使我们能够确定贝叶斯估计策略，这些策略结合了良好的性能以及就高斯状态和测量而言直接进行实验实现的潜力。我们的结果为采用局部估计技术的不确定性提供了实用的解决方案，从而缩小了可以采用渐近最优策略的制度的差距。