We present the entanglement measures of a tetrapartite W-class entangled system in a 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 π 4 and Π 4 , are studied and illustrated with graphics through their dependence 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 π-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 . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.

Chinese Physics BJul 1, 201917 citations

Tetrapartite entanglement features of W-Class state in uniform acceleration

Qian Dong, Ariadna J. Torres-Arenas, Guo-Hua Sun +1 more

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 π 4 and geometric Π 4 average of tangles. Notice that the difference between π 4 and Π 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 κξ and S κζδ with two and three involved noninertial qubits first increases and then decreases with the acceleration parameter r , but they are equal to constants 1 and 0.811278 respectively for zero involved noninertial qubit.

arXiv:1911.03399Frontiers of PhysicsNov 16, 201931 citations