Abstract We consider the sensing of scalar valued fields with specific spatial dependence using a network of sensors, e.g. multiple atoms located at different positions within a trap. We show how to harness the spatial correlations to sense only a specific signal, and be insensitive to others at different positions or with unequal spatial dependence by constructing a decoherence-free subspace for noise sources at fixed, known positions. This can be extended to noise sources lying on certain surfaces, where we encounter a connection to mirror charges and equipotential surfaces in classical electrostatics. For general situations, we introduce the notion of an approximate decoherence-free subspace, where noise for all sources within some volume is significantly suppressed, at the cost of reducing the signal strength in a controlled way. We show that one can use this approach to maintain Heisenberg-scaling over long times and for a large number of sensors, despite the presence of multiple noise sources in large volumes. We introduce an efficient formalism to construct internal states and sensor configurations, and apply it to several examples to demonstrate the usefulness and wide applicability of our approach.

中文翻译：

---

分布式传感的近似去相干自由子空间

摘要我们考虑使用传感器网络来感知具有特定空间依赖性的标量值场，例如位于陷阱内不同位置的多个原子。我们展示了如何利用空间相关性来仅感知特定信号，并且通过在固定的已知位置为噪声源构建无退相干子空间来对不同位置或具有不相等空间依赖性的其他信号不敏感。这可以扩展到位于某些表面上的噪声源，我们在经典静电学中遇到与镜像电荷和等势表面的连接。对于一般情况，我们引入了近似无退相干子空间的概念，其中某个体积内所有源的噪声都被显着抑制，代价是以受控方式降低信号强度。我们表明，尽管存在大量的多个噪声源，但人们可以使用这种方法在长时间和大量传感器上保持海森堡缩放。我们引入了一种有效的形式来构建内部状态和传感器配置，并将其应用于几个示例，以证明我们方法的有用性和广泛适用性。