Role of nonclassical temporal correlation in powering quantum random access codes

We explore the fundamental origin of quantum advantage behind random access code. propose new temporal inequalities compatible with noninvasive-realist models and show that any nonzero $n\ensuremath{\mapsto}1$ code in presence shared randomness is equivalent to violation corresponding inequality. As a consequence this connection, we also prove maximal success probability can be obtained when inequality achieved. further code, or other words, inequality, certify genuine randomness.