On global states of collections of random variables

FEDERICO HOLIK

Praga

Workshop; The 4th workshop Quantum Contextuality in Quantum Mechanics and Beyond (QCQMB); 2021

One of the characteristic traits of quantum theory is that the description of a quantum systeminvolves a collection of incompatible measurement contexts. Each context can be seen as a classicalrandom variable, defined by a complete set of commuting observables. But it turns out thatcontexts are intertwined: quantum probabilistic models can be described as very specific pastingsof Boolean algebras, which are globally non-Boolean. States are represented by density operatorsthat define global states, and give place to classical probabilities when restricted to the maximalBoolean subalgebras associated to measurement contexts. The characterization of the peculiarpasting occurring in the quantum domain has been a topic of much research, and is related to theunderstanding of quantum contextuality. In this talk we discuss different techniques for combiningcollections of (possibly non-compatible) random variables in such a way that one obtains ?as inthe quantum case? a global state that yields classical probabilities when restricted to the localBoolean subalgebras. After commenting different approaches related to the possibility of usingnegative 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 representingstates of contextual probabilistic theories.