Optimal quantum-state tomography with known parameters

Abstract

It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.