Flexible quantum state tomography

We present an efficient algorithm that solves the quantum state tomography problem from an arbitrary number of projective measurements in any finite dimension $d$. The algorithm is flexible enough to allow us to impose any desired rank $r$ to the state to be reconstructed, ranging from pure ($r=1$) to full rank $(r=d)$ quantum states. The method exhibits successful and fast convergence under the presence of realistic errors in both state preparation and measurement stages, and also when considering overcomplete sets of observables. We demonstrate that the method outperforms semidefinite programming quantum state tomography for some sets of physically relevant quantum measurements in every finite dimension.