We consider non-local sensing of scalar signals with specific spatial dependence in the Bayesian regime. We design schemes that allow one to achieve optimal scaling and are immune to noise sources with a different spatial dependence than the signal. This is achieved by using a sensor array of spatially separated sensors and constructing a multi-dimensional decoherence free subspace. While in the Fisher regime with sharp prior and multiple measurements only the spectral range Δ is important, in single-shot sensing with broad prior the number of available energy levels L is crucial. We study the influence of L and Δ also in intermediate scenarios, and show that these quantities can be optimized separately in our setting. This provides us with a flexible scheme that can be adapted to different situations, and is by construction insensitive to given noise sources.

中文翻译：

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贝叶斯体制中的噪声分布感知

我们考虑在贝叶斯体制中具有特定空间依赖性的标量信号的非局部感测。我们设计的方案可以实现最佳缩放，并且不受与信号相比具有不同空间依赖性的噪声源的影响。这是通过使用空间上分离的传感器的传感器阵列并构建多维无相干的子空间来实现的。在费舍尔制中，先验和多次测量非常重要，仅光谱范围Δ是重要的，而先验传感的先验条件广泛，可用能级L的数量至关重要。我们还在中间场景中研究了L和Δ的影响，并表明可以在我们的设置中分别优化这些数量。这为我们提供了可以适应不同情况的灵活方案，