Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration

Using the single-mode approximation, we study entanglement measures including two independent quantities; i.e., negativity and von Neumann entropy for a tripartite generalized Greenberger–Horne–Zeilinger (GHZ) state in noninertial frames. Based on the calculated negativity, we study the whole entanglement measures named as the algebraic average \pi_3-tangle and geometric average \it \Pi_3-tangle. We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits. The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers. The results show that there will always exist entanglement, even if acceleration r arrives to infinity. The degree of entanglement for all 1–1 tangles are always equal to zero, but 1–2 tangles always decrease with the acceleration parameter r. We notice that the von Neumann entropy increases with the number of the accelerated observers and S_\kappa_\rm I\zeta_\rm I (\kappa, \zeta\in (\rm A, B, C)) first increases and then decreases with the acceleration parameter r. This implies that the subsystem \rho_\kappa_\rm I\zeta_\rm I is first more disorder and then the disorder will be reduced as the acceleration parameter r increases. Moreover, it is found that the von Neumann entropies S_\rm ABCI, S_\rm ABICI and S_\rm AIBICI always decrease with the controllable angle \theta, while the entropies of the bipartite subsystems S_2-2_\rm non (two accelerated qubits), S_2-1_\rm non (one accelerated qubit) and S_2-0_\rm non (without accelerated qubit) first increase with the angle \theta and then decrease with it.