QM Research Seminar: Ordered Vector Spaces and Hierarchies in Quantum Information

Speaker: Martin Plávala (University of Siegen)


Abstract:

We review recent results on tensor products of the ordered vector spaces: we show that the tensor product is almost never uniquely defined due to the existence of entanglement between any non-classical (non-simplical) cones, and we present a hierarchy of convex optimization programs that aim to determine whether a given vector is entangled or not. We then apply these abstract mathematical results to two problems in quantum information: semi-device independent certification of Schmidt rank and semi-device independent certification of number of incompatible measurements, where we obtain hierarchies of outer approximation by semi-definite programming problems. Moreover we show that these outer approximations yield bounds that are relevant for potential experimental implementations. Finally we discuss other applications of the presented abstract hierarchies to problems in quantum information and other fields.