Realistic limits on the nonlocality of an N -partite single-photon superposition
Amine Laghaout, Gunnar G. Bjork, Ulrik L. Andersen · Physical Review A · 2011
A recent paper [L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, New J. Phys. 13, 053054 (2011)] revealed that a single quantum symmetrically delocalized over $N$ modes, namely a $W$ state, effectively allows for all-versus-nothing proofs of nonlocality in the limit of large $N$. Ideally, this finding opens up the possibility of using the robustness of the $W$ states while realizing the nonlocal behavior previously thought to be exclusive to the more complex class of Greenberger-Horne-Zeilinger states. We show that in practice, however, the slightest decoherence or inefficiency of the Bell measurements on $W$ states will degrade any violation margin gained by scaling to higher $N$. The nonstatistical demonstration of nonlocality is thus proved to be impossible in any realistic experiment.