Tetrapartite entanglement features of W-Class state in uniform acceleration

Abstract

Using the single-mode approximation, we first calculate entanglement measures such as negativity ($1-3$ and $1-1$ tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual $\pi_{4}$ and geometric $\Pi_{4}$ average of tangles. Notice that the difference between $\pi_{4}$ and $\Pi_{4}$ is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration $r$ tends to infinity. The degree of entanglement is disappeared for the $1-1$ tangle case when the acceleration $r > 0. 472473$. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy $S$ of the total system always increases with the increasing accelerated observers, but the $S_{\kappa\xi}$ and $S_{\kappa\zeta\delta}$ with two and three involved noninertial qubits first {\it increases} and then {\it decreases} with the acceleration parameter $r$, but they are equal to constants $1$ and $0. 811278$ respectively for zero involved noninertial qubit.