Sufficient conditions for quantum advantage in random access code protocols with twoqubit states
Abstract
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 sharedinadvance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of singlebit communication and with a shared arbitrary state of two qubits. Taking the worstcase 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.
 Publication:

Physical Review A
 Pub Date:
 July 2023
 DOI:
 10.1103/PhysRevA.108.012617
 arXiv:
 arXiv:1912.09900
 Bibcode:
 2023PhRvA.108a2617K
 Keywords:

 Quantum Physics
 EPrint:
 7 pages, 1 figure, accepted version