  The aim of this paper is to analyze the reconstructability of quantum
mechanics from classical conditional probabilities representing measurement
outcomes conditioned on measurement choices. We will investigate how the
quantum mechanical representation of classical conditional probabilities is
situated within the broader frame of noncommutative representations. To this
goal, we adopt some parts of the quantum formalism and ask whether empirical
data can constrain the rest of the representation to conform to quantum
mechanics. We will show that as the set of empirical data grows conventional
elements in the representation gradually shrink and the noncommutative
representations narrow down to the unique quantum mechanical representation.
