Strong supremacy of quantum systems as communication resource

Abstract

We investigate the task of $d$-level random access codes ($d$-RACs) and consider the possibility of encoding classical strings of $d$-level symbols (dits) into a quantum system of dimension $d'$ strictly less than $d$. We show that the average success probability of recovering one (randomly chosen) dit from the encoded string can be larger than that obtained in the best classical protocol for the task. Our result is intriguing as we know from Holevo's theorem (and more recently from Frenkel-Weiner's result [Commun. Math. Phys. 340, 563 (2015)]) that there exist communication scenarios wherein quantum resources prove to be of no advantage over classical resources. A distinguishing feature of our protocol is that it establishes a stronger quantum advantage in contrast to the existing quantum $d$-RACs where $d$-level quantum systems are shown to be advantageous over their classical $d$-level counterparts.