Inferring Quantum Network Topology using Local Measurements

TL;DR

This paper introduces a protocol that uses entropic measures and measurement covariance to efficiently infer and distinguish the topology of quantum networks, even in noisy conditions and without prior topological knowledge.

Contribution

It presents a novel, noise-robust protocol leveraging entropic quantities and covariance for quantum network topology inference, applicable with minimal assumptions.

Findings

Covariance-based methods outperform entropy in accuracy and efficiency.

Entropy measures effectively identify the absence of entanglement.

Protocol is implementable via quantum variational optimization.

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.