We show a quantum state with explicit local hidden-variable models for correlations between any fixed number of subsystems which cannot be extended to a model simultaneously describing correlations between different numbers of subsystems. The explicit models we discuss may involve several settings per observer and the way to disqualify them involves only two settings per party.

• Received 18 June 2012

DOI:https://doi.org/10.1103/PhysRevA.86.032105