Simple and general bounds on quantum random access codes

TL;DR

This paper derives general bounds on the success probabilities of quantum random access codes, extending known results and providing approximations for complex cases in quantum information science.

Contribution

It introduces new bounds for quantum random access codes involving multiple variables and dimensions, generalizing previous specific results.

Findings

Bounds recover known special cases

Numerical analysis shows bounds provide good approximations

Bounds are not tight but still useful

Abstract

Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a D-dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.