Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames

Understand

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.