Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration
Qian Dong1, M. A. Mercado Sanchez1, Guo-Hua Sun2, Mohamad Toutounji3, Shi-Hai Dong1**
1Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, UPALM, CDMX 07700, Mexico 2Catedrática CONACyT, Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, CDMX 07738, Mexico 3Department of Chemistry, P. O. Box 15551, UAE University, Al Ain, UAE
Abstract：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.
2019, Vol. 36 
