The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for constructing efficient sensing networks, is that of the role of inter-sensor correlations in the simultaneous estimation of multiple linear functions, where the latter are taken over a collection local parameters and can thus be seen as global properties. In this work we provide a solution to this when each node is a qubit and the state of the network is sensor-symmetric. First we derive a general expression linking the amount of inter-sensor correlations and the geometry of the vectors associated with the functions, such that the asymptotic error is optimal. Using this we show that if the vectors are clustered around two special subspaces, then the optimum is achieved when the correlation strength approaches its extreme values, while ther...

中文翻译：

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用于估计线性函数的量子感测网络

在过去的几年中，网络量子感测的理论框架得到了很大的发展，但是仍然存在许多悬而未决的问题。其中，从根本上和对于构建有效的传感网络而言，重要的问题是传感器间相关性在同时估计多个线性函数中的作用，其中线性函数接管了集合局部参数，因此可以被视为全局属性。在这项工作中，当每个节点都是一个量子位并且网络的状态是传感器对称的时，我们将提供一个解决方案。首先，我们导出一个通用表达式，将传感器之间的相关程度和与函数相关的矢量的几何形状联系起来，从而使渐近误差最佳。