Preparation contextuality as an essential feature underlying quantum communication advantage

The study of ontology (hidden variables) provides for a vital ground on which significant nonclassical features of quantum theory are revealed. One such nonclassical ontic feature is preparation contextuality (PC) and advantage in oblivious communication tasks is one of its operational signatures. This article primarily pursues the ontic feature underlying quantum advantage in communication complexity (CC). We construct oblivious communication tasks tailored to given CC problems. We upper bound the classical success probability of these oblivious communication tasks, obtaining preparation noncontextual inequalities. We use the very states and measurements responsible for advantage in CC problems along with the orthogonal mixtures of these states to orchestrate an advantageous protocol for the associated oblivious communication tasks and the violation of the associated inequalities, thereby unveiling PC. To showcase the vitality of our results, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems.

Figure 1

Construction of OC task based on a given $\mathcal{\text{CC}}$ task. Notice while the amount of communication in the $\mathcal{\text{CC}}$ task by the dimension $d$ of the physical system, there is no such constraint on communication in the $\mathcal{\text{OC}}$. Instead, the communication is restricted so as not to reveal any information about the oblivious variable $x$.

Figure 2

Alternative construction of OC task based on a given CC task. The communication is restricted so as not to reveal any information about a oblivious variable $y$.