Relaxed uncertainty relations and information processing

Details Relaxed uncertainty relations and information processing Relaxed uncertainty relations and information processing

2008-11-23

arxiv.org/abs/0811.3771v2

Quantum Information and Computation, 9 (9&10), 0801-0832, 2009

Physics

Quantum Physics

33 pages, 1 figure. v2: improved notation, to appear in QIC

Scientific paper

We consider a range of "theories" that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty relation, and that relaxing this relation allows for non-local correlations that are stronger than what can be obtained in quantum mechanics. We continue to construct a hierarchy of related non-signaling theories, and show that on one hand they admit superstrong random access encodings and exponential savings for a particular communication problem, while on the other hand it becomes much harder in these theories to learn a state. We show that the existence of these effects stems from the absence of certain constraints on the expectation values of commuting measurements from our non-signaling theories that are present in quantum theory.

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