Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames

We apply genuine multipartite entanglement concurrence to investigate entanglement properties of Dirac fields in noninertial frames. We present analytical concurrences for bipartite and tripartite entanglements simultaneously, which enriches previous results. We note that the entanglement of the Greenberger-Horne-Zeilinger-like state is degraded by the Unruh effect, but this entangled system always remains entangled to a degree and can be used in quantum teleportation between parties in relatively uniform acceleration. We find that all tripartite subsystems in noninertial frames are monogamous in that they all satisfy Coffmann-Kundu-Wootters monogamous inequality. We also find two useful relations regarding concurrences.

Figure 1

Plots of concurrence $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{I}}{\mathrm{C}}_{\mathrm{I}}}\right)$ as functions of $r_b$ and $r_c$ when Alice remains stationary while Rob and Charlie accelerate uniformly. $\left|\alpha \right|=1/2$ (dashed blue line); $\left|\alpha \right|=1/\sqrt{2}$ (solid red line); $\left|\alpha \right|=\sqrt{7/8}$ (dotted brown line). (a) For $r_b=\pi /6,r_c=r$ and (b) for $r_b=r_c=r$.

Figure 2

Plots of concurrence $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{II}}{\mathrm{C}}_{\mathrm{II}}}\right)$ as functions of $r_b$ and $r_c$ when Alice remains stationary while Rob and Charlie accelerate uniformly. $\left|\alpha \right|=1/2$ (dashed blue line); $\left|\alpha \right|=1/\sqrt{2}$ (thick red line); $\left|\alpha \right|=\sqrt{7/8}$ (dotted brown line). (a) For $r_b=\pi /6,r_c=r$ and (b) for $r_b=r_c=r$.

Figure 3

Plots of concurrence $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{I}}{\mathrm{B}}_{\mathrm{II}}}\right),C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AC}}_{\mathrm{I}}{\mathrm{C}}_{\mathrm{II}}}\right)$ and $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{B}}_{\mathrm{I}}{\mathrm{B}}_{\mathrm{II}}}\right),C_{\mathrm{GM}}\left({\rho }_{{\mathrm{C}}_{\mathrm{I}}{\mathrm{C}}_{\mathrm{II}}}\right)$ as functions of $r_b$ and $r_c$ when Alice remains stationary while Rob and Charlie accelerate uniformly. $\left|\alpha \right|=1/2$ (dashed blue line); $\left|\alpha \right|=1/\sqrt{2}$ (solid red line); $\left|\alpha \right|=\sqrt{7/8}$ (dotted brown line).

Figure 4

Plots of concurrence $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{I}}{\mathrm{C}}_{\mathrm{II}}}\right),C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{II}}{\mathrm{C}}_{\mathrm{I}}}\right)$ as functions of $r_b$ and $r_c$ when Alice remains stationary while Rob and Charlie accelerate uniformly. $\left|\alpha \right|=1/2$ (dashed blue line); $\left|\alpha \right|=1/\sqrt{2}$ (solid red line); $\left|\alpha \right|=\sqrt{7/8}$ (dotted brown line). (a) $r_b=\pi /6,r_c=r$ for $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{I}}{\mathrm{C}}_{\mathrm{II}}}\right)$; $r_b=r,r_c=\pi /6$ for $C_{\mathrm{GM}}\left({\rho }_{{\mathrm{AB}}_{\mathrm{II}}{\mathrm{C}}_{\mathrm{I}}}\right)$. (b) For $r_b=r_c=r$.