Instituto de Física La Plata (CONICET), Argentina, olentiev2@gmail.com
One of the characteristic traits of quantum theory is that the description of a quantum system involves a collection of incompatible measurement contexts. Each context can be seen as a classical random variable, defined by a complete set of commuting observables. But it turns out that contexts are intertwined: quantum probabilistic models can be described as very specific pastings of Boolean algebras, which are globally non-Boolean. States are represented by density operators that define global states, and give place to classical probabilities when restricted to the maximal Boolean subalgebras associated to measurement contexts. The characterization of the peculiar pasting occurring in the quantum domain has been a topic of much research, and is related to the understanding of quantum contextuality. In this talk we discuss different techniques for combining collections of (possibly non-compatible) random variables in such a way that one obtains –as in the quantum case– a global state that yields classical probabilities when restricted to the local Boolean subalgebras. After commenting different approaches related to the possibility of using negative probabilities, we address the well known problem of pasting families of Boolean algebras. We discuss some of our findings with regard to the problem of defining global objects representing states of contextual probabilistic theories.