## Higher order interference versus quantum theory

We (Ududec, Barnum, and Emerson) adapt Rafael Sorkin's hierarchy of

orders of interference in physical theories to the framework of

"general probabilistic theories", defining a notion of k-path

interference experiment and of k-th order coherence in such theories

and showing that k-th order interference in such an experiment is

equivalent to k-th order coherence between faces of the state spaces

associated with paths in the experiment. We also show that

Jordan-algebraic theories have at most second-order interference (the