Preparation contextuality: the ground of quantum communication advantage
Debashis Saha, Anubhav Chaturvedi · arXiv (Cornell University) · 2018
Where does quantum advantage spring from? Such an investigation necessitates invoking an ontology on which non-classical features of quantum theory are explored. One such non-classical ontic-feature is preparation contextuality (PC) and advantage in oblivious communication tasks is its operational signature. In this letter, we deal with quantum advantage in communication which has two prominent manifestations, advantage in communication complexity (CC) and device independent information processing based on violation of Bell inequalities. First, we demonstrate that quantum advantage in one-way CC operationally reveals PC. Specifically, we construct oblivious communication tasks tailored to one-way CC problems. The bound on classical success probability in the oblivious communication tasks forms our preparation non-contextual inequalities. We use the same states along with their orthogonal mixtures and measurements responsible for advantage in one-way CC problems to orchestrate an advantageous protocol for the oblivious communication tasks and the violation of the associated inequalities. Further, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems. Second, we prove that (spatial and temporal) Bell-inequality violation implies an advantage in oblivious communication tasks, thereby revealing PC. Along with the implications of this work, we discuss other known indications towards our assertion that PC is the fundamental non-classical feature underlying quantum advantage.