The aim of this talk is to develop some theory around bistochastic operators and majorization in the context of operator-valued measurable functions, that is quantum random variables. To this end one needs to define an $L^1$ norm for such functions and develop a weak topology. Once this is all in place, I will show how to characterize majorization in terms of certain kinds of permutation-invariant convex functions.

This is joint work with Sarah Plosker (Brandon).