We show that Connes' embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.
We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). We show that matrix norms and accretive cones are induced by gauges, although inducing gauges are not unique in general. Finally, we show that completely positive completely contractive linear maps on non-unital operator spaces extend to any containing operator system if and only if the operator space is induced by a unique gauge.
We provide a complete geometric description of the set of synchronous quantum correlations for the three-experiment two-outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be realized using projection valued measures on a Hilbert space of dimension no more than 16.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.