From quantum tomography to phase retrieval and back

This letter is devoted to the cross-fertilization between the fields of phase retrieval and quantum tomography. In the first part we discuss topological aspects of quantum tomography which turn out to imply lower bounds on the number of frame vectors necessary to reconstruct signals modulo phase. In the second part we generalize the approach of Balan, Casazza and Edidin to construct frames for phase retrieval to the context of quantum tomography. In this process we obtain an extension of their result to Parseval frames.