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On equivalence between Popescu-Rohrlich boxes and random access codes

Thursday 26th September 2013 - 13:30 to 14:30
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons