Network tomography refers to the use of inference techniques for inferring internal network states from end-to-end probes. Quantum probes, implemented by sending blocks of $n$ coherent-state pulses augmented with continuous-variable (CV) squeezing ($n=1$) or weak temporal-mode entanglement ($n>1$) over a lossy channel to a receiver with homodyne detection capabilities, are known to carry information about the channel transmissivity. Assuming a subset of nodes in an optical network is capable of sending and receiving such probes through intermediate nodes with all-optical switching capabilities, we leverage these quantum probes to estimate link transmissivities. To determine how to route the probes in a network, we propose a probe construction algorithm that guarantees link identifiability, while maximizing the number of information orthogonal sets of transmissivities. A set of probes induces a Fisher information matrix (FIM). We then derive two metrics, the determinant of the FIM and the trace of its inverse, to evaluate the performance of the probes. In particular, our results can be used to characterize the quantum improvement in estimating link transmissivities in a general optical network.

翻译：网络断层扫描指通过端到端探测推断内部网络状态的推理技术。量子探测通过向具备零差检测能力的接收器发送经连续变量压缩（$n=1$）或弱时域模纠缠（$n>1$）增强的$n$个相干态脉冲块，在损耗信道中传递信息，已知能携带信道透射率信息。假设光网络中部分节点可通过具有全光交换能力的中间节点发送和接收此类探测，我们利用这些量子探针来估计链路透射率。为确定网络中探测路由策略，我们提出一种保证链路可辨识性，同时最大化信息正交透射率集合数量的探测构建算法。一组探测构成费舍尔信息矩阵。据此我们推导出两个度量指标——费舍尔信息矩阵的行列式及其逆矩阵的迹——来评估探测性能。特别地，我们的结果可用于表征一般光网络中链路透射率估计的量子改进特性。