Entanglement Certification by Measuring Nonlocality

TL;DR

This paper introduces a practical method for verifying quantum entanglement in networks by measuring nonlocality through CHSH inequality violations, providing bounds, resource analysis, and simulation tools for reliable certification.

Contribution

It offers new fidelity bounds from CHSH measurements, a sample-complexity analysis, and verification protocols with mathematical guarantees, advancing entanglement certification in quantum networks.

Findings

Fidelity bounds derived from CHSH violations enable entanglement certification.

Sample complexity analysis quantifies measurement requirements for confidence levels.

Simulation framework explores trade-offs in resource-constrained quantum network verification.

Abstract

Reliable verification of entanglement is a central requirement for quantum networks. This paper presents a practical verification approach based on violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality. We derive tight mathematical bounds that relate the CHSH value to entanglement fidelity and introduce a statistical framework that optimizes resource usage while ensuring reliable certification. Our main contributions are: (i) fidelity bounds derived directly from the CHSH measure, which also enable nonlocality certification at sufficiently high fidelities; (ii) a sample-complexity analysis that quantifies the number of measurements required to achieve desired confidence levels for the CHSH measure and the entanglement fidelity; and (iii) verification protocols, some with rigorous mathematical guarantees and others with numerical evaluation. Using NetSquid, we develop a simulation framework that models diverse network conditions and enables systematic exploration of trade-offs in CHSH-based verification. This framework highlights the interplay between accuracy, efficiency, and operational parameters, providing concrete guidelines for deploying entanglement verification in resource-constrained quantum networks.