Intraparticle entanglement-based Random Access Code protocols: Contextuality-enabled quantum advantage and implications

We provide the first explicit identification and quantitative characterization of the physical origin of the quantum advantage in the Random Access Code (RAC) protocol.

This is achieved by formulating the protocol in terms of intraparticle entanglement between co-measurable degrees of freedom of a single particle and establishing a fundamental correspondence between the protocol's success probability and the underlying resource powering it.

For this purpose, we use a relevant Bell-type inequality derived from the assumption of noncontextuality of measurement outcomes.

The formulated analysis reveals that the magnitude of quantum-mechanical violation of this inequality, signifying a form of quantum contextuality, is quantitatively commensurate with the ``quantum enhancement" of success probability in any intraparticle entanglement-assisted $n$-bit RAC protocol.

In particular, the maximal success probability achievable in a quantum $n \mapsto 1$ RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality.

Our framework not only demonstrates how quantum contextuality entailed by intraparticle entanglement serves as an effective resource for enhancing RAC performance, but also offers a significant operational advantage: the proposed scheme is readily implementable in a single-particle interferometric setup requiring coherence preservation only for a single particle, rather than between spatially separated entangled systems.