One Parameter family of N-qudit Werner-Popescu states: Bipartite separability using conditional quantum relative Tsallis entropy

TL;DR

This paper uses the conditional sandwiched Tsallis relative entropy to determine bipartite separability of N-qudit Werner-Popescu states, providing a necessary and sufficient criterion that outperforms previous methods.

Contribution

It introduces the CSTRE criterion for bipartite separability, demonstrating its theoretical superiority over Abe-Rajagopal entropy in analyzing N-qudit Werner-Popescu states.

Findings

CSTRE matches algebraic method in separability range

Limit q→∞ provides strongest separability constraint

CSTRE converges faster than Abe-Rajagopal entropy

Abstract

The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner- Popescu states in their 1 : N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit q tending to infinity and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe- Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.