Tetrapartite entanglement measures of W-Class in noninertial frames

TL;DR

This paper investigates how entanglement in a four-part W-Class quantum system behaves under noninertial conditions, revealing that entanglement persists in most cases but diminishes with acceleration, and providing analytical entropy expressions.

Contribution

It introduces new measures of tetrapartite W-Class entanglement in noninertial frames, analyzing their dependence on acceleration and deriving analytical entropy formulas.

Findings

Negativity and $ ext{pi}$-tangle decrease with acceleration but remain nonzero.

The $1-1$ tangle vanishes at infinite acceleration in the first case.

Analytical von Neumann entropy increases with acceleration.

Abstract

We present the entanglement measures of a tetrapartite W-Class entangled system in noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The $1-1$ tangle, $1-3$ tangle and whole entanglement measurements ($\pi_4$ and $\Pi_4$), are studied and illustrated with graphics through their dependency on the acceleration parameter $r_d$ for the first case and $r_c$ and $r_d$ for the second case. It is found that the Negativities ($1-1$ tangle and $1-3$ tangle) and $\pi$-tangle decrease when the acceleration parameter $r_{d}$ or in the second case $r_c$ and $r_d$ increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the $1-1$ tangle for the first case, vanishes at infinite accelerations, but for the second case the $1-1$ tangle disappears completely when $r>0.472473$. It is found an analytical expression for von Neumann information entropy of the system and we notice that it increases with the acceleration parameter.