Persistence of tripartite nonlocality for noninertial observers

We consider the behavior of bipartite and tripartite nonlocality between fermionic entangled states shared by observers, one of whom uniformly accelerates. We find that while fermionic entanglement persists for arbitrarily large acceleration, the Bell–Clauser-Horne-Shimony-Holt inequalities cannot be violated for sufficiently large but finite acceleration. However, the Svetlichny inequality, which is a measure of genuine tripartite nonlocality, can be violated for any finite value of the acceleration.

Figure 1

The maximal value of the left-hand side of the Svetlichny inequality plotted against Rob's acceleration $r$ and the control parameter ${\theta }_1$ for the GGHZ state. As ${\theta }_1$ increases, so does the $\pi$ tangle of the state.

Figure 2

The maximal value of $S\left({\psi }_M\right)$ plotted as a function of the control parameter ${\theta }_3$ and Rob's acceleration $r$, with Rob measuring qubit 2.