Joint GOA/QLunch: Alexander Müller-Hermes
Speaker: Alexander Müller-Hermes, University of Oslo
Title: Monogamy of entanglement between cones
Abstract: A separable quantum state shared between parties A and B can be symmetrically extended to a quantum state shared between party A and parties B1,...,Bk for every natural number k. Entangled quantum states do not have this property. This phenomenon is known as “monogamy of entanglement”. We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones CA and CB: The elements of the minimal tensor product are precisely the tensors in CA\otimes_max CB that can be symmetrically extended to elements in the maximal tensor product CA\otimes_max CB1\otimes_max ...\otimes_max CBk for every k. It is a natural question when the minimal tensor product CA\otimes_min CB coincides with the set of k-extendible tensors for some finite k. We show that this is universally the case for every cone CA if and only if CB is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest.
Joint work with Guillaume Aubrun and Martin Plavala. For more information see: