The fourtangle in the transverse XY model

TL;DR

This paper investigates the four-tangle measure in the transverse XY model, revealing its limitations and the need for additional entanglement measures to identify GHZ-type entanglement.

Contribution

It provides a detailed analysis of the four-tangle measure in the XY model and highlights its insufficiency for detecting GHZ-type entanglement, suggesting the use of supplementary measures.

Findings

C4 measure is non-zero in the XY model, comparable to genuine negativity.

C4 alone cannot guarantee GHZ_4-type entanglement.

Observed interference effects in C4 related to concurrence.

Abstract

We analyze the entanglement measure $C_4$ for mixed states in general and for the transverse XY model. We come to the conclusion that it cannot serve alone for guaranteeing an entanglement of $GHZ_4$-type. The genuine negativity calculated in Ref.~\cite{Hofmann14} isn't sufficient for that either and some additional measure of entanglement must be considered. In particular we study the transverse XY-model and find a non-zero $C_4$ measure which is of the same order of magnitude than the genuine negativity. Furthermore, we observe a feature in the $C_4$ values that resembles a destructive interference with the underlying concurrence.