Sufficient Conditions for the Non-Contextuality of Correlation Functions

Piotr Badziąg, Ingemar Bengtsson, Adán Cabello +1 more

Giovanni Carù

The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to sheaf cohomology, which provides a sufficient condition for contextuality of empirical models in quantum mechanics and beyond. Subsequently, a number of studies proposed methods to detect contextuality based on different cohomology theories. However, none of these cohomological descriptions succeeds in giving a full invariant for contextuality applicable to concrete examples. In the present work, we introduce a cohomology invariant for possibilistic and strong contextuality which is applicable to the vast majority of empirical models.

Chellasamy Jebarathinam, R. Srikanth

Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we characterize nonclassical quantum correlation beyond contextuality, in terms of supernoncontextuality, namely the higher-than-quantum hidden-variable (HV) dimensionality required to reproduce the given noncontextual quantum correlations. Thus supernoncontextuality is the contextuality analogue of superlocality. Specifically, we study the quantum system of two-qubit states in a scenario composed of five contexts that demonstrate contextuality in a state-dependent fashion. For this purpose, we use the framework of boxes, whose behavior is described by a set of probabilities satisfying the no-disturbance conditions. We first demonstrate that while superlocality is necessary to observe a contextual box, superlocality is not sufficient for contextuality. On the other hand, a noncontextual superlocal box can be supernoncontextual, but superlocality is not a necessary condition. We then introduce a notion of nonclassicality beyond the standard contextuality, called semi-device-independent contextuality. We study semi-device-independent contextuality of two-qubit states in the above-mentioned scenario and demonstrate how supernoncontextuality implies this nonclassicality. To this end, we propose a criterion and a measure of semi-device-independent contextuality.

Leonardo Silva Vieira Santos

In the present master's thesis we study logical contextuality and inequality-free proofs of quantum contextuality and nonlocality.The former concept can be understood as the possibilistic version of contextuality, while the latter refers to proofs of quantum probabilistic non-classicalities that are not based on violation of any noncontextuality (or Bell) inequality.The present work aims to build a bridge between these two concepts through what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality.As our main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios.We discuss some consequences arising from the completeness of such possibilistic paradoxes.Finally, we review some inequality-free proofs under the light of the developed formalism.

A.P. Costa, Fernando Parisio