Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy

TL;DR

This paper demonstrates that negative conditional Tsallis relative entropy indicates entanglement in bipartite quantum states and precisely characterizes separability ranges for symmetric N-qubit states, aligning with PPT criteria.

Contribution

It introduces a method using conditional Tsallis entropy to determine bipartite separability ranges, matching established criteria and highlighting advantages of non-commuting entropy.

Findings

Negative conditional Tsallis entropy implies entanglement.

Exact separability ranges match PPT criterion for symmetric states.

Non-commuting Tsallis entropy offers advantages in entanglement detection.

Abstract

In any bipartition of a quantum state, it is proved that the negative values of the conditional version of sandwiched Tsallis relative entropy necessarily implies quantum entanglement. For any N, the separability ranges in the $1:N-1$ partition of symmetric one parameter families of noisy $N$-qubit W, GHZ, states are determined using the conditional quantum relative Tsallis entropy approach. The 1:N-1 separability range matches exactly with the range obtained through positive partial transpose criterion, for all N. The advantages of using non-commuting version of $q$-conditional relative Tsallis entropy is brought out through this and other one-parameter families of states.