When Are Popescu-Rohrlich Boxes and Random Access Codes Equivalent?

TL;DR

This paper investigates the conditions under which PR-boxes and random access codes are equivalent resources, establishing that non-signaling racboxes can simulate PR-boxes, while signaling racboxes cannot, thus clarifying their interconvertibility.

Contribution

It introduces the concept of racbox and demonstrates the equivalence of non-signaling racboxes and PR-boxes, providing a resource inequality and exploring the limits of simulation.

Findings

Non-signaling racboxes can simulate PR-boxes.

Signaling racboxes cannot simulate PR-boxes.

Resource inequality between racboxes and PR-boxes is saturated.

Abstract

We study a problem of interconvertibility of two supra-quantum resources: one is so called PR-box, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It has been known, that PR-box supplemented with one bit of communication can be used to simulate RAC. We ask the converse question: to what extent RAC can simulate PR-box? To this end we introduce racbox: a box such that supplemented with one bit of communication offers RAC. As said, PR-box can simulate racbox. The question we raise, is whether any racbox can simulate PR-box. We show that a non-signaling racbox indeed can simulate PR-box, hence those two resources are equivalent. We also provide an example of signalling racbox which cannot simulate PR-box. We give a resource inequality between racbox es and PR-boxes, and show that it is saturated.