Towards a minimal example of quantum nonlocality without inputs

Abstract

The network scenario offers interesting new perspectives on the phenomenon of quantum nonlocality. Notably, when considering networks with independent sources, it is possible to demonstrate quantum nonlocality without the need for measurements inputs, i.e. with all parties performing a fixed quantum measurement. Here we aim to find minimal examples of this effect. Focusing on the minimal case of the triangle network, we present examples involving output cardinalities of $3-3-3$ and $3-3-2$. Finally, we discuss the prospects of finding an example of quantum nonlocality in the triangle network with binary outputs, and point out a connection to the Lovasz local lemma.

In the initial version of our manuscript, we discovered a mistake in the proof of Theorem 2. Consequently, in the updated version, Theorem 2 has been revised. Furthermore, in Appendix C, we include an updated proof applicable to a broader range of entangled states

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• Topologically Robust Quantum Network Nonlocality
• Noise-robust proofs of quantum network nonlocality
• Experimental quantum triangle network nonlocality with an AlGaAs multiplexed entangled photon source
• 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
• Violation of the Finner inequality in the four-output triangle network
• Guarantees on the structure of experimental quantum networks
• Exploring the Local Landscape in the Triangle Network
• Quantum non-classicality in the simplest causal network
• Experimental genuine quantum nonlocality in the triangle network