Tetrapartite entanglement measures of GHZ state with nonuniform acceleration

Using the single-mode approximation, we first calculate entanglement measures such as negativity and von Neumann entropy for a tetrapartite GHZ entangled system in nonuniform acceleration frame. We then analyse the whole entanglement measures, the algebraic residual measure π₄ and geometric average measure Π₄. We find that the difference between π₄ and Π₄ is very slight or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from two accelerated observers and others remaining stationary to all four accelerated observers, which are accelerated in nonuniform acceleration. The results presented here show that there still exists entanglement 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 verify the existence of the Unruh effect even in nonuniform acceleration frame. It is also found that the von Neumann entropy increases with the increasing accelerated observers. It is interesting to see that S₂ and S₃ with two and three involved noninertial qubits first increase and then decrease with the acceleration parameter r, but S₂ is equal to constant 1 for zero involved noninertial qubit. The special cases in the limit r_a,b,c,d → π/4 are also studied.