Inferring Quantum Network Topology Using Local Measurements

Daniel T. Chen, Brian Doolittle, Jeffrey Larson, Zain H. Saleem, Eric Chitambar

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number040347
JournalPRX Quantum
Volume4
Issue number4
DOIs
StatePublished - Oct 2023
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • General Computer Science
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics
  • Electrical and Electronic Engineering

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