  Sequences of compatible quantum measurements can be contextual and any
simulation with a classical model accounting for the quantum observations,
needs to use some internal memory. In Ref. [New J. Phys. 13, 113011 (2011)], it
was shown that simulating the sequences of compatible observables from the
Peres-Mermin scenario requires at least three different memory states in order
to be not in contradiction with the deterministic predictions of quantum
theory. We extend this analysis to the probabilistic quantum predictions and
ask how much memory is required to simulate the quantum correlations generated
by any quantum state. We find, that even in this comprehensive approach only
three internal states are required for the perfect simulation of the quantum
correlations in the Peres-Mermin scenario.
