Communication games measure preparation contextuality

A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality whenever its predictions cannot be explained by a preparation noncontextual model. Here, we show that the ability of an operational theory to perform communication games is a measure of the degree of preparation contextuality in that theory. For statistics obtained in a particular family of communication games, we show a direct correspondance with correlations in space-like separated events obeying the no-signaling principle. Using this, we prove that all mixed quantum states of any finite dimension are preparation contextual. We present an experimental realization of a communication game involving three-level quantum systems from which we observe a strong violation of the constraints of preparation noncontextuality.