We prove that quantum random access code (QRAC) performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for QRAC provides a semi-device independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for QRAC and earlier quantities introduced to assess incompatibility.
@article{arxiv.1911.04360,
title = {Quantum random access codes and incompatibility of measurements},
author = {Claudio Carmeli and Teiko Heinosaari and Alessandro Toigo},
journal= {arXiv preprint arXiv:1911.04360},
year = {2020}
}