Inferring Quantum Network Topology using Local Measurements

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.

References in corpus (28)

• Quantum entanglement
• Quantum Computing in the NISQ era and beyond
• The Quantum Internet
• Three qubits can be entangled in two inequivalent ways
• Variational Quantum Algorithms
• Entanglement detection
• Evaluating analytic gradients on quantum hardware
• Robustness of entanglement
• Towards a global quantum network
• Qubit teleportation between non-neighboring nodes in a quantum network
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Bell nonlocality in networks
• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
• Nonlinear Bell inequalities tailored for quantum networks
• Polynomial Bell inequalities
• Limits on correlations in networks for quantum and no-signaling resources
• Entanglement Classification via Neural Network Quantum States
• Semidefinite tests for quantum network topologies
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Design and Implementation of the Illinois Express Quantum Metropolitan Area Network
• Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
• Characterizing Quantum Networks: Insights from Coherence Theory
• Analysing causal structures with entropy
• Semidefinite tests for latent causal structures
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Quantum violation of local causality in urban network with hybrid photonic technologies

Cited by in corpus (4)

• Certifying the Topology of Quantum Networks: Theory and Experiment
• Topologically Robust Quantum Network Nonlocality
• A Review of Software for Designing and Operating Quantum Networks
• Error-mitigated inference of quantum network topology