Non-local correlations as an information theoretic resource

Abstract

It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are non-local, in the sense that a Bell inequality is violated. They cannot, however, be used for super-luminal signalling. It is also known that it is possible to write down sets of ``super-quantum'' correlations that are more non-local than is allowed by quantum mechanics, yet are still non-signalling. Viewed as an information theoretic resource, super-quantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signalling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signalling polytope in the case that two observers each choose from two possible measurements with d outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.