# All entangled pure quantum states violate the bilocality inequality

## TL;DR

This paper demonstrates that all entangled pure states violate the bilocality inequality and establishes a link between CHSH violation and bilocality violation for mixed states, advancing understanding of quantum correlations in networks.

## Contribution

It provides a complete characterization of pure states violating bilocality and a general criterion for mixed states, connecting bilocality violation with CHSH inequality.

## Key findings

- All entangled pure states violate the bilocality inequality.
- Any entangled state violating CHSH also violates the bilocality inequality.
- Derived a criterion for bilocality violation in mixed two-qubit states.

## Abstract

The nature of quantum correlations in networks featuring independent sources of entanglement remains poorly understood. Here, focusing on the simplest network of entanglement swapping, we start a systematic characterization of the set of quantum states leading to violation of the so-called "bilocality" inequality. First, we show that all possible pairs of entangled pure states can violate the inequality. Next, we derive a general criterion for violation for arbitrary pairs of mixed two-qubit states. Notably, this reveals a strong connection between the CHSH Bell inequality and the bilocality inequality, namely that any entangled state violating CHSH also violates the bilocality inequality. We conclude with a list of open questions.