Partial self-testing and randomness certification in the triangle network

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.

5+22 pages, 4 figures

References in corpus (9)

• Beyond Bell's Theorem: Correlation Scenarios
• Bell nonlocality in networks
• Information-Theoretic Implications of Quantum Causal Structures
• Full network nonlocality
• Single-photon nonlocality in quantum networks
• Nonlocality for Generic Networks
• Towards a minimal example of quantum nonlocality without inputs
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• A convergent inflation hierarchy for quantum causal structures

Cited by in corpus (15)

• Certification of non-classicality in all links of a photonic star network without assuming quantum mechanics
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Which features of quantum physics are not fundamentally quantum but are due to indeterminism?
• Quantum coherence in networks
• Post-quantum nonlocality in the minimal triangle scenario
• Network quantum steering enables randomness certification without seed randomness
• Topologically Robust Quantum Network Nonlocality
• Noise-robust proofs of quantum network nonlocality
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• Operationally independent events can influence each other in quantum theory
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Local models and Bell inequalities for the minimal triangle network
• Experimental genuine quantum nonlocality in the triangle network
• Quantum non-classicality in the simplest causal network