Entanglement-assisted random access codes

An (n,m,p) random access code (RAC) makes it possible to encode n bits in an m-bit message in such a way that a receiver of the message can guess any of the original n bits with probability p greater than 1/2. In quantum RACs (QRACs), one transmits n qubits. The full set of primitive entanglement-assisted random access codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any n an (n,1,p) EARAC. QRACs for n>3 exist only if parties also share classical randomness. We show that EARACs outperform the best of known QRACs not only in the success probabilities but also in the amount of communication needed in the preparatory stage of the protocol. Upper bounds on the performance of EARACs are given and shown to limit also QRACs.