Random Access Code protocols: Quantum advantage related to intraparticle entanglement-based contextuality

TL;DR

This paper demonstrates that intraparticle entanglement-induced quantum contextuality directly correlates with quantum advantage in Random Access Code protocols, linking quantum resources to protocol success.

Contribution

It establishes a quantitative connection between intraparticle entanglement-based contextuality and quantum advantage in RAC protocols using a single-particle framework.

Findings

Quantum violation of Bell-type inequality matches RAC success probability

Maximal success probability aligns with maximal quantum violation

Single-particle interferometric setup can empirically test the predictions

Abstract

The quantum enhancement of success probability in the Random Access Code (RAC) protocols remains unexplored from two important perspectives. First, the use of entanglement between two co-measurable degrees of freedom of a single particle (intraparticle entanglement) in achieving such quantum enhancement has not been investigated. Second, no explicit quantitative correspondence has been established between the predicted/observed quantum advantage and the underlying quantum resource responsible for it. In this work, we address both these aspects simultaneously by harnessing a single-particle resource. For this purpose, the RAC protocol is formulated in terms of intraparticle entanglement between, for instance, spin/polarization and path degrees of freedom of a single particle. Within this framework, a relevant Bell-type inequality, derived from the assumption of noncontextuality for single particle path-spin measurements, is used. Based on these ingredients, the formulated analysis reveals that the magnitude of quantum-mechanical violation of such Bell-type 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 of a quantum $n \mapsto 1$ RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality. This correspondence is empirically testable using a readily implementable single-particle interferometric setup requiring coherence preservation only for a single particle.