Speaker
Francesca la Piana, University of Oslo
Abstract
In the classical setting, the Birkhoff–von Neumann theorem states that every doubly stochastic matrix can be written as a convex combination of permutation matrices. In the quantum setting, this analogy fails. Motivated by this failure, as well as by questions arising in the study of quantum automorphisms of graphs, we introduce the “”Graph Quantum Magic Squares””, obtained by imposing an additional graph constraint on quantum magic squares. We show that the corresponding analogue of the Birkhoff–von Neumann theorem already fails for the cyclic graph C_4, via an explicit counterexample. We also prove that Graph Quantum Magic Squares admit monic linear matrix inequality descriptions, and hence form compact free spectrahedra.