  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.
