  We implement an experiment on a photonic quantum processor establishing
efficacy of an elementary quantum system in classical information storage. The
advantage is established by considering a class of simple bipartite games
played with the communication resource qubit and classical bit (c-bit),
respectively. Conventional wisdom, as articulated by the no-go theorems of
Holevo and Frenkel-Weiner, suggests that such a quantum advantage is
unattainable in scenarios wherein sender and receiver possess shared randomness
or classical correlation between them. Notably, the advantage we report is
demonstrated in a scenario where participating players lack any form of shared
randomness. Our experiment involves the development of a variational triangular
polarimeter, enabling the realization of positive operator value measurements
crucial for establishing the targeted quantum advantage. In addition to
demonstrating a robust communication advantage of a single qubit our experiment
also opens avenues for immediate applications in near-term quantum
technologies. Furthermore, it constitutes a semi-device-independent
non-classicality certification scheme for the quantum encoding-decoding
apparatus, underscoring the broader implications of our work beyond its
immediate technological applications.
