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We study a problem of interconvertibility of two supra-quantum resources: oneis so called PR-box, which violates CHSH inequality up to maximal algebraicbound, and second is so called random access code (RAC). The latter is afunctionality 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 canbe used to simulate RAC. We ask the converse question: to what extent RAC cansimulate PR-box? To this end we introduce racbox: a box such that supplementedwith 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 thata non-signaling racbox indeed can simulate PR-box, hence those two resourcesare equivalent. We also provide an example of signalling racbox which cannotsimulate PR-box. We give a resource inequality between racbox es and PR-boxes,and show that it is saturated.

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