Exploring the Local Landscape in the Triangle Network

• URL: http://arxiv.org/abs/2405.08939v1
• Date: Tue, 14 May 2024 20:09:35 GMT
• Title: Exploring the Local Landscape in the Triangle Network
• Authors: Elisa Bäumer, Victor Gitton, Tamás Kriváchy, Nicolas Gisin, Renato Renner,
• Abstract summary: We investigate inner approximations of the set of local (classical) distributions of the triangle network. A quantum distribution that appears to be nonlocal is the Elegant Joint Measurement (EJM) We find a remarkable agreement between analytical and neural-network-based inner approximations. Our results considerably strengthen the conjecture that the EJM is nonlocal.
• Score: 1.3514953384460016
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Characterizing the set of distributions that can be realized in the triangle network is a notoriously difficult problem. In this work, we investigate inner approximations of the set of local (classical) distributions of the triangle network. A quantum distribution that appears to be nonlocal is the Elegant Joint Measurement (EJM) [Entropy. 2019; 21(3):325], which motivates us to study distributions having the same symmetries as the EJM. We compare analytical and neural-network-based inner approximations and find a remarkable agreement between the two methods. Using neural network tools, we also conjecture network Bell inequalities that give a trade-off between the levels of correlation and symmetry that a local distribution may feature. Our results considerably strengthen the conjecture that the EJM is nonlocal.

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