  The optimal success probability of a communication game sets fundamental
limitations on an operational theory. Quantum advantage of parity oblivious
random access code (PORAC), a communication game, over classical resources
reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102,
010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite
dimensions is an open problem. Here, we show that the degree of uncertainty
allowed in an operational theory determines the amount of preparation
contextuality. We connect the upper bound of fine-grained uncertainty relation
to the success probability of PORAC game played with the quantum resource.
Subsequently, we find the optimal success probability for the 2-dit PORAC game
using MUBs for the decoding strategy. Finally, we also derive an upper bound on
quantum advantage for the N-dit PORAC game.
