Communication Games Reveal 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 communication games performed in operational theories reveal the preparation contextuality of that theory. For statistics obtained in a particular family of communication games, we show a direct correspondence with correlations in spacelike separated events obeying the no-signaling principle. Using this, we prove that all mixed quantum states of any finite dimension are preparation contextual. We report on 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.

Figure 1

Experimental setup. Suitable settings of ${\chi }_1$ and ${\chi }_2$ allow us to produce the desired qutrit states for the task. Measurement basis selection is implemented by appropriate settings of HWPs ${\theta }_1$, ${\theta }_2$, and ${\theta }_3$ and by setting the total experimental phase (${\varphi }_i;i\in 1,2,3$) between path modes by employing a phase shifter box (QWP-HWP-QWP) inside the setup. Detection events in detectors $|\alpha ⟩$, $|\beta ⟩$, and $|\gamma ⟩$ are used to obtain the respective probabilities.