Classical and quantum memory in contextuality scenarios

Abstract

Quantum theory can be described as a framework for calculating probabilities of measurement outcomes. A great part of its deep foundational questions comes from the fact that these probabilities may disagree with classical calculations, under reasonable premises. Theclassical notion in which the observables are frequently assumed as predened before their measurement motivates the assumption of noncontextuality, i.e. that all the observables have preassigned values before the interaction with the experimental apparatus, independently onwhich other observables are jointly measured with it. It is known that this classical view is inconsistent with quantum predictions. The main question of this thesis can be phrased as: can we use memory to classically obtain results in agreement with quantum theory applied to sequential measurements? If so, how to quantify the amount of memory needed? These questions are addressed in a specic contextuality scenario: the Peres-Mermin square. Previous results are extended by using a comprehensive scheme, which shows that the same bound of a threeinternal- state automaton is sucient, even when all probabilistic predictions are considered. Trying to use a lower dimensional quantum resource, i.e. the qubit, to reduce the memory cost in this scenario led us to another question of whether or not there is contextuality for this typeof system. We nd that sequences of compatible and repeatable quantum measurements on a qubit cannot reveal contextuality, even when the measurements are not assumed projective beforehand.