Nature of Nonlocality in a triangle network based on EJM

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in[Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In[npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, we find the nature of the correlation in a triangle network scenario. We here observe how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here we use the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. We also check the probability bound for the polygon structure.