Optimal Monitor Placement in Quantum Network Tomography

Monitoring the performance of internal network elements is crucial for network management and optimizing network operations. Quantum Network Tomography (QNT) focuses on the characterization of quantum channels through end-to-end measurements between selected subsets of network nodes. In this work, we examine optimal strategies for monitor placement in QNT. Our study specifically targets a four-node quantum star network in which links are modelled as depolarizing channels. We investigate QNT methods that utilize a single monitor in the four-node star network, and evaluate estimation performance for all possible monitor placements in the star network. We perform a theoretical analysis of the estimators by calculating the Quantum Fisher information matrix (QFIM) and the Quantum Cramer-Rao Bound (QCRB). The QCRB provides a lower bound on the variance of any estimator, thereby offering a benchmark for their efficiency. We identify the monitor placement at the hub as a baseline to analyze the performance of end-to-end estimation given that the monitor has direct access to every link of the network. Through further investigation, we find that the best performance is achieved by placing the monitor in the leaf with the least noisy link for the 4- node star network.