Sufficient conditions for quantum advantage in random access code protocols with two-qubit states

A random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n -bit string, while only having limited information about the n -bit string. Quantum RACs usually utilize either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with a shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with an invertible correlation matrix can be used to outperform the best classical RAC for n =3 . We derive an additional condition sufficient to beat the best classical performance in the case of n =2 . In particular, separable states turn out to be a useful resource behind the quantum advantage for n =2 ,3 . For n ≥4 , RACs assisted with a single copy of a quantum state do not outperform the classical RACs.