  Communication games are collaborative information processing tasks involving
a number of players with limited communication. Such games are useful tools for
studying physical theories. A physical theory exhibits preparation
contextuality whenever observed behaviour cannot be explained by a preparation
noncontextual model. Here we show that there is a fundamental connection
between the performance in communication games and the degree of preparation
(non)contextuality. For this purpose, we present a general framework that
allows us to construct communication games such that the game performance
corresponds to a measure of preparation (non)contextuality. We illustrate the
power of this framework by, 1) deriving many examples of tests of preparation
contextuality, 2) showing that quantum violations of Bell inequalities can be
derived from quantum violations of preparation noncontextuality, 3)
qualitatively and quantitatively explaining related previous results on
preparation contextuality in quantum communication games, and 4) solving the
open problem of revealing the preparation contextuality of the maximally mixed
quantum state in any dimension.
