Relaxed uncertainty relations and information processing
arXiv:0811.3771
Abstract
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.
33 pages, 1 figure. v2: improved notation, to appear in QIC
References in corpus (9)
- Non-local correlations as an information theoretic resource
- A limit on nonlocality in any world in which communication complexity is not trivial
- General properties of Nonsignaling Theories
- A generalized no-broadcasting theorem
- Monogamy of nonlocal quantum correlations
- Implications of Superstrong Nonlocality for Cryptography
- Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
- Monogamy of Bell correlations and Tsirelson's bound
- Generalized Bloch Spheres for m-Qubit States