An Optimization Framework for Monitor Placement in Quantum Network Tomography

TL;DR

This paper develops an optimization framework for monitor placement in quantum network tomography, enhancing channel estimation accuracy and scalability through ILP formulations and multi-monitor strategies.

Contribution

It introduces two ILP-based methods for optimal monitor placement in quantum networks, improving estimation performance and scalability over prior single-monitor approaches.

Findings

Multi-monitor placement can match hub-monitor performance in star networks.

QMF optimization balances estimation accuracy with monitoring overhead.

The framework is applicable to star and tree-structured quantum networks.

Abstract

Quantum Network Tomography (QNT) offers a framework for end-to-end quantum channel characterization by strategically placing monitor nodes within the network. Building upon prior work on single-monitor placement, we study optimal monitor placement and measurement assignments for channel parameter estimation in arbitrary quantum networks. Using an n-node star network as a baseline, we analyze multi-monitor configurations and show that distributing monitors across end nodes can achieve estimation performance comparable to a monitor placed at the hub. Estimation precision is quantified using the Quantum Fisher Information Matrix (QFIM), with channel parameters inferred via Maximum Likelihood Estimation (MLE) and benchmarked against the Quantum Cramer-Rao Bound (QCRB). To generalize, we develop two Integer Linear Program (ILP) formulations: one maximizing estimation accuracy (QF), and another jointly optimizing accuracy and monitoring overhead (QMF). Unlike QF, QMF prevents monitor overloading, enabling scalability and parallelism. We prove optimality for star and analyze applicability to tree-structured quantum networks.