Low rank matrix recovery from Clifford orbits

Understand

We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group.

• As a special case, our theory makes statements about the phase retrieval problem.
• Here, the task is to recover a vector given only the amplitudes of its inner product with a small number of vectors from an orbit.
• Variants of the group in question have appeared under different names in many areas of mathematics.