Tetrapartite entanglement measures of GHZ state with uniform acceleration

Using the single-mode approximation, we calculate entanglement measures such as negativity (1 - 3, 1 - 1 and 2 - 2 tangles) and von Neumann entropy for a tetrapartite Greenberger-Horne-Zeilinger system in a non-inertial frame. We then analyze the whole entanglement measures, the residual π ₄ and geometric Π₄ average of tangles. We find that the difference between them is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer and others remaining stationary to all four accelerated observers. The results presented here show that entanglement still exists for the complete system even when acceleration r tends to infinity. The degree of entanglement is always equal to zero for the 1 - 1 tangle case. We also study the negativity 2 - 2 tangle for completeness. We reexamine the existence of the Unruh effect in non-inertial frames. It is also found that the von Neumann entropy increases with the increasing accelerated observers, and S κ I ζ I and S κ I ζ Iδ I first increase and then decrease with the acceleration parameter r, e.g. Sκ ζ max )=1.65853 at r = 0.599881 and Sκ ζ δ(max )=2.28231 at r = 0.676196. This implies that the subsystems ρ κ I ζ I and ρ κ I ζ I δ I are at first more disordered and then the disorder is reduced with the increasing acceleration parameter r.