Quantal and semi-classical approaches to the degradation of quantum reference frames

There has been much recent activity in the study of quantum reference frames, from their role as resources in quantum information theory to their role in the application of superselection rules. These studies make it clear that we must carefully distinguish cases in which we take a reference frame for granted from those in which we include the physical reference frame in our dynamics. In this talk I will describe the degradation of a quantum reference frame as it is used to make repeated measurements, where the entangling of the frame and the system under study results in an increasingly mixed state for the frame which is decreasingly useful as a reference. We show that the `longevity' of the frame as a useful reference scales quadratically with the `strength' of that frame. I will also describe a recent semi-classical approach to the degradation of a directional reference frame where it is modelled as a random walk on the sphere.