Adaptive Rank Quantum State Estimation
Quantum state estimation is an important task in the realm of experimental quantum information science. While the common approaches to this task are generally adequate, the maximum-likelihood method is frequently used with parameterizations that do not strictly satisfy the statistical requirements of maximum-likelihood estimation. We show that the source of this issue is in the structure of the parameter space and we introduce a density matrix parameterization that provides direct control over this structure. The parameterization leads to a natural quantum state estimation algorithm that does satisfy the statistical requirements of maximum-likelihood estimation. Finally, we examine the algorithm through the analysis of several data sets and experimental results.