Cloning and Broadcasting in Generic Probabilistic Theories
Howard N. Barnum‚ Jonathan Barrett‚ M. S. Leifer and Alexander Wilce
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially \backslashem any non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.