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On equivalence between Popescu-Rohrlich boxes and random access codes

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Mathematical Challenges in Quantum Information

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 racboxes and PR-boxes, and show that it is saturated.

This talk is part of the Isaac Newton Institute Seminar Series series.

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