Complementarity between entanglement-assisted and quantum distributed random access code

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of $3 rightarrow 1$ distributed RACs cite{network} and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa.Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the $3 rightarrow 1$ distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.