Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states

TL;DR

This paper investigates the nonlocality and entanglement properties of three-qubit GHZ-symmetric states, revealing that genuine tripartite entanglement does not necessarily imply nonlocality, with some states being fully local.

Contribution

It provides a complete characterization of SLOCC classes within GHZ-symmetric states and shows that genuine tripartite entanglement does not guarantee nonlocality.

Findings

Some GHZ-symmetric states are fully local despite being in the biseparable region.

Bilocal states exist within both W and GHZ classes.

Genuine tripartite entanglement does not ensure genuine nonlocality.

Abstract

The hierarchy of nonlocality and entanglement in multipartite systems is one of the fundamental problems in quantum physics. We study this topic in three-qubit systems considering the entanglement classification of stochastic local operations and classical communication (SLOCC). The equivalence under SLOCC divides threequbit states into separable, biseparable, W, and Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as a research subject, which share the symmetries of the GHZ state and have a complete characterization of SLOCC classes. In the biseparable region (with bipartite entanglement), there exist GHZ-symmetric states that are found to be fully local. In addition, there are bilocal states in both theW and GHZ classes. That is, neither of the subclasses of genuine tripartite entanglement can ensure genuinely tripartite nonlocality.