Transfer of nonlocality and entanglement of an open three-qubit W state in the background of dilaton black hole

Abstract

Constrained by the complexity of theoretical calculations, current research on genuine tripartite nonlocality (GTN) within the relativistic framework concentrates mainly on Greenberger-Horne-Zeilinger-like states, with few studies addressing W states or even general tripartite states. In this paper, we apply numerical methods to investigate how environmental decoherence and spacetime dilaton influence GTN and genuine tripartite entanglement (GTE) of W states. Our results show that GTN in the physically accessible region displays a ``sudden death phenomenon'' and that sufficiently strong decoherence completely destroys GTN. By contrast, GTE in the physically accessible region initially remains unchanged and then decays only when the dilaton parameter becomes large. Notably, the GTN and GTE in the physically accessible region can be enhanced by adjusting the decoherence parameter. Furthermore, we also find that the GTN in the physically inaccessible region cannot be generated, whereas the GTE will be produced there. This implies that GTE can cross the event horizon of a black hole and realize the redistribution of quantum entanglement. Finally, we further discuss whether the GTN can be transferred to the bipartite subsystem of the system.

Figures (10)

• Figure 1: (a) GTN $S(\rho_{AB_IC_I})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for r=0.05, p=0.05(red solid line), r=0.1, p=0.1 (green dashed line) and r=0.5, p=0.5 (blue dashed line). (b) GTN $S(\rho_{AB_IC_I})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.05$, $p=0.05$ (red solid line), $r=0.05$, $p=0.5$ (green dashed line) and $r=0.05$, $p=0.9$ (blue dashed line).
• Figure 2: (a) GTE $E(\rho_{AB_IC_I})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.1$, $p=0.5$ (green dashed line), $r=0.5$, $p=0.5$ (blue dashed line) and $r=0.7$, $p=0.5$ (red solid line). (b) GTE $E(\rho_{AB_IC_I})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.5$, $p=0.05$ (green dashed line), and $r=0.5$, $p=0.9$ (red solid line).
• Figure 3: (a) GTN $S(\rho_{AB_IB_{II}})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.05$, $p=0.05$ (red solid line), $r=0.1$, $p=0.1$ (green dashed line) and $r=0.5$, $p=0.5$ (blue dashed line). (b) GTE $E(\rho_{AB_IB_{II}})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.1$, $p=0.5$ (green dashed line), $r=0.5$, $p=0.5$ (blue dashed line) and $r=0.7$, $p=0.5$ (red solid line).
• Figure 4: (a) GTE $E(\rho_{AB_IB_{II}})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.3$, $p=0.1$ (green dashed line), and $r=0.3$, $p=0.9$ (red solid line). (b) GTE $E(\rho_{AB_IB_{II}})$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.7$, $p=0.1$ (green dashed line), and $r=0.7$, $p=0.9$ (red solid line).
• Figure 5: (a) GTN $S(\rho_{AB_{II}C_{II}} )$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.05$, $p=0.05$ (red solid line), $r=0.1$, $p=0.1$ (green dashed line) and $r=0.5$, $p=0.5$ (blue dashed line). (b) GTE $E(\rho_{AB_{II}C_{II}} )$ of the three-qubit system as a function of the dilaton parameter $\alpha$ with $\omega=1$, $M=1$ for $r=0.1$, $p=0.5$ (green dashed line), $r=0.4$, $p=0.5$ (blue dashed line) and $r=0.6$, $p=0.5$ (red solid line).