  The classical phase retrieval problem arises in contexts ranging from speech
recognition to x-ray crystallography and quantum state tomography. The
generalization to matrix frames is natural in the sense that it corresponds to
quantum tomography of impure states. We provide computable global stability
bounds for the quasi-linear analysis map $\beta$ and a path forward for
understanding related problems in terms of the differential geometry of key
spaces. In particular, we manifest a Whitney stratification of the positive
semidefinite matrices of low rank which allows us to ``stratify'' the
computation of the global stability bound. We show that for the impure state
case no such global stability bounds can be obtained for the non-linear
analysis map $\alpha$ with respect to certain natural distance metrics.
Finally, our computation of the global lower Lipschitz constant for the $\beta$
analysis map provides novel conditions for a frame to be generalized phase
retrievable.
