Memory cost for simulating all quantum correlations of the Peres-Mermin scenario

TL;DR

This paper investigates the minimal classical memory needed to simulate quantum correlations in the Peres-Mermin scenario, showing that only three internal states suffice for perfect simulation, even with probabilistic predictions.

Contribution

It extends previous deterministic results to probabilistic quantum predictions, demonstrating that three internal states are sufficient for simulating all quantum correlations in this scenario.

Findings

Three internal states are enough for perfect simulation.

Probabilistic quantum correlations do not increase memory requirements.

Classical simulation complexity is bounded by three states.

Abstract

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.