Noise-resilient quantum random access codes

A ${n}^{d}\stackrel{p}{\ensuremath{\rightarrow}}1$ quantum random access code (QRAC) is a communication task where Alice encodes $n$ classical bits into quantum states of dimension $d$ and transmits them to Bob, who performs appropriate measurements to recover the required bit with probability $p$. In the presence of a noisy environment, the performance of a QRAC is degraded, losing the advantage over classical strategies. We propose a practical technique that enables noise tolerance in such scenarios, recovering the quantum advantage in retrieving the required bit. We perform a photonic implementation of a ${2}^{2}\stackrel{\text{p}}{\ensuremath{\rightarrow}}1$ QRAC using polarization-encoded qubits under an amplitude-damping channel, where simple operations allow for noise robustness showing the revival of the quantum advantage when the noisy channel degrades the performance of the QRAC. This revival can be observed by violating a suitable dimension witness, which is closely related to the average success probability of the QRAC. This technique can be extended to other applications in the so-called prepare-and-measure scenario, enhancing the semi-device-independent protocol implementations.