  A recent paper [L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, New
Journal of Physics, 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 (GHZ) 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 non-statistical demonstration of nonlocality is thus proved to be
impossible in any realistic experiment.
