Quantum reference frame resources and monotones

Random unitary channels (RUC) can impose superselection rules (SSR) on states that pass through them. This is the case, for example, when two parties lack a shared reference frame (RF) for the physical degree of freedom in which information is encoded. Such situations give rise to a new kind of quantum information resource, dubbed "frameness", that can be used to overcome the ensuing SSR-constraints. We introduce a family of monotones for the frameness associated with phase RFs , and show further that this family is closely related to generalized concurrence functions of entangled states. We use one of these monotones to determine the explicit analytical form of a qubit's "frameness of formation". The frameness of formation is a measure of the average cost of preparing the qubit in units of frameness known as "refbit". Finally we go over an iterative protocol for distilling the frameness associated with phase and parity RFs.