QLunch: Alex Müller-Hermes

Every multipartite entangled quantum state becomes fully separable after an entanglement breaking quantum channel acted locally on each of its subsystems. Whether there are other quantum channels with this property is an open problem with important implications for entanglement theory. We cast this problem in the general setting of proper convex cones in finite-dimensional vector spaces. The entanglement annihilating maps transform the k-fold maximal tensor product of a cone C_1 into the k-fold minimal tensor product of a cone C_2, and the pair (C_1,C_2) is called resilient if all entanglement annihilating maps are entanglement breaking. Our main result is that the pair (C_1,C_2) is resilient if C_1 or C_2 is a Lorentz cone. To show this result we consider the regularization of the injective-to-projective tensor norms of operators between finite-dimensional normed spaces, called the tensor radius, and we show that it coincides with the nuclear norm if either of the involved normed spaces is Euclidean. In the case of the identity operator this property characterizes Euclidean spaces and we conjecture that this is the case in general. This is joined work with Guillaume Aubrun.