Maximal Overlap with a Fully Separable State and Translational Invariance in Multipartite Entangled States

TL;DR

This paper investigates how translational invariance influences the maximal overlap with fully separable states in multipartite entangled states, providing exact and numerical results for one-dimensional qubit systems.

Contribution

It introduces a hierarchy of translationally invariant entangled states and offers methods to determine maximal overlaps and nearest fully separable states.

Findings

Translational invariance affects the maximal overlap and separable states.

Hierarchy of translationally invariant entangled states established.

Methods for finding maximal overlaps in specific systems provided.

Abstract

The maximal overlap with the fully separable state for the multipartite entangled pure state with translational invariance is studied explicitly by some exact and numerical evaluations, focusing on the one-dimensional qubit system and some representative types of translational invariance. The results show that the translational invariance of the multipartite state could have an intrinsic effect on the determinations of the maximal overlap and the nearest fully separable state for multipartite entangled states. Furthermore a hierarchy of the basic entangled states with translational invariance is founded, from which one could readily find the maximal overlap and a related fully separable state for the multipartite state composed of different translational invariance structures.