Quantum random access codes and incompatibility of measurements

TL;DR

This paper shows that quantum random access codes outperform classical ones only with incompatible measurements, providing a semi-device independent test for quantum incompatibility and linking success probability to measurement incompatibility.

Contribution

It establishes a direct link between QRAC performance and measurement incompatibility, offering a new semi-device independent method to detect quantum incompatibility.

Findings

QRAC outperforms classical codes with incompatible measurements

Any incompatible projective measurements improve success probability

Connection between QRAC success and measurement incompatibility measures

Abstract

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.