Bounding the persistency of the nonlocality of W states
Péter Diviánszky, Réka Trencsényi, Erika Bene, Tamás Vértesi · Physical Review A · 2016
The nonlocal properties of the $W$ states are investigated under particle loss. By removing all but two particles from an $N$-qubit $W$ state, the resulting two-qubit state is still entangled. Hence, the $W$ state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality [see N. Brunner and T. V\'ertesi, Phys. Rev. A 86, 042113 (2012)]. Namely, we inquire what is the minimal number of particles that must be removed from the $W$ state so that the resulting state becomes local. We bound this value in function of $N$ qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between $2N/5$ and $N/2$ for large $N$. We also develop a framework to establish bounds for more than two settings per site.