Violating the bilocal inequality with separable mixed states in the entanglement-swapping network

TL;DR

This paper investigates whether separable mixed states can violate the bilocal inequality in entanglement-swapping networks, using Particle Swarm Optimization to identify such states, revealing that some separable states can indeed violate the inequality.

Contribution

It demonstrates that certain separable mixed states can violate the bilocal inequality, expanding understanding of quantum correlations beyond entangled states.

Findings

Separable mixed states can violate the bilocal inequality.

Particle Swarm Optimization effectively identifies violating states.

Some states are separable yet violate the inequality.

Abstract

It has been showed that two entangle pure states can violate the bilocal inequality in the entanglement-swapping network, vice versa. What happens for mixed states? Whether or not are there separable mixed states violating the bilocal inequality? In the work, we devote to finding the mixed Werner states which violate the bilocal inequality by Particle Swarm Optimization (PSO) algorithms. Finally, we shows that there are pairs of states, where one is separable and the other is entangled, can violate the bilocal inequality.