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The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph theory, leading to a beautiful geometric characterization of such sets. This geometry can also be explored in the definition of contextuality quantifiers based on geometric distances, which is important for the resource theory of contextuality, developed after the recognition of contextuality as a potential resource for quantum computation. In this paper we review the geometric aspects of contextuality and use it to define several quantifiers, which have the advantage of being applicable to the exclusivity approach to contextuality, where previously defined quantifiers do not fit.
Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two contexts overlap
It is well known that certain measurement scenarios behave in a way which can not be explained by classical theories but by quantum theories. This behaviours are usually studied by Bell or non-contextuality (NC) inequalities. Knowing the maximal clas
In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in quantum-optics problems.
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an extreme form of