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

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.

10 pages, 4 figures

References in corpus (5)

• Semi-device-independent security of one-way quantum key distribution
• The mother of all protocols: Restructuring quantum information's family tree
• Entanglement Theory and the Second Law of Thermodynamics
• Bound non-locality and activation
• Extrema of discrete Wigner functions and applications

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