Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach

TL;DR

This paper investigates the separability of symmetric W and GHZ multiqubit states using Tsallis q-conditional entropy, demonstrating that the q-->infinity limit provides a stronger separability criterion than von Neumann entropy.

Contribution

It introduces a q-conditional entropy approach to analyze multiqubit state separability, showing improved limitations over traditional von Neumann entropy methods.

Findings

q-->infinity limit yields the strongest separability condition

Method provides sufficient but not necessary conditions for most states

Enhanced detection of entanglement compared to von Neumann entropy

Abstract

We employ conditional Tsallis q entropies to study the separability of symmetric one parameter W and GHZ multiqubit mixed states. The strongest limitation on separability is realized in the limit q-->infinity, and is found to be much superior to the condition obtained using the von Neumann conditional entropy (q=1 case). Except for the example of two qubit and three qubit symmetric states of GHZ family, the $q$-conditional entropy method leads to sufficient - but not necessary - conditions on separability.