Title: Inferring Quantum Network Topology using Local Measurements Show Chinese title

Title: 使用局部测量推断量子网络拓扑

Abstract: Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities -- namely, the von Neumann entropy and the measured mutual information -- as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime. Show Chinese abstract

Abstract: 量子网络中节点之间可以生成的统计相关性在很大程度上取决于其拓扑结构。 然而，这种拓扑信息可能事先并不知道，或者可能需要进行验证。 在本文中，我们提出了一种高效的协议，用于区分和推断量子网络的拓扑结构。 我们利用熵量——即冯·诺依曼熵和测量互信息——以及测量协方差来唯一地表征拓扑结构。 我们证明，熵量足以区分两个制备GHZ态的网络。 此外，如果可以获得量子比特测量结果，那么熵量和协方差都可以用来推断网络拓扑结构，而无需假设状态制备。 我们表明，该协议对噪声具有完全的鲁棒性，并可以通过量子变分优化实现。 在经典模拟器和量子硬件上的数值实验表明，协方差通常在准确且高效地推断拓扑结构方面更可靠，而基于熵的方法在低样本情况下通常更擅长识别纠缠的缺失。