Spatial versus Sequential Correlations for Random Access Coding

TL;DR

This paper explores the duality in quantum random access codes, comparing spatial correlations violating Bell inequalities with sequential correlations from quantum channels, revealing different performance limits and advantages.

Contribution

It introduces tailored Bell inequalities for the task and analyzes their violations, highlighting the distinct roles of spatial and sequential quantum correlations in random access coding.

Findings

Spatial and sequential quantum correlations impose different performance limits.

Sequential correlations can outperform classical strategies where spatial correlations cannot.

Some random access codes show no advantage from spatial correlations but benefit from sequential correlations.

Abstract

Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality, or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here, we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes. We also show that there exist random access codes for which spatial quantum correlations offer no gain over classical strategies, whereas sequential quantum correlations can yield an advantage. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.