Partial self-testing and randomness certification in the triangle network

TL;DR

This paper demonstrates that in triangle quantum networks, nonlocal correlations can be partially self-tested, leading to certifiable randomness and requirements for entanglement and entropy in sources and measurements.

Contribution

It introduces a method to self-test quantum strategies in ring networks and applies it to the triangle network, establishing conditions for genuine nonlocality and randomness certification.

Findings

Nonlocal correlations in the triangle network require minimal entanglement in sources.

Local measurements must be entangled to produce nonlocal correlations.

Each local outcome contains a minimal amount of entropy, certifying randomness.

Abstract

Quantum nonlocality can be demonstrated without inputs (i.e. each party using a fixed measurement setting) in a network with independent sources. Here we consider this effect on ring networks, and show that the underlying quantum strategy can be partially characterized, or self-tested, from observed correlations. Applying these results to the triangle network allows us to show that the nonlocal distribution of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)] requires that (i) all sources produce a minimal amount of entanglement, (ii) all local measurements are entangled, and (iii) each local outcome features a minimal entropy. Hence we show that the triangle network allows for genuine network quantum nonlocality and certifiable randomness.