Using prior information for continuous measurement quantum state reconstruction.

Density matrices representing quantum states must be positive.~ This restriction can provide crucial information for a quantum state-tomography procedure, allowing one to reconstruct states for which there is otherwise insufficient information.~ We explain the use of semidefinite programming techniques to enforce the positivity constraint and present an example of its use in the course of quantum state reconstruction by continuous weak measurement.~ Both simulated and experimental results for the reconstruction will be discussed for a variety of states~of a spin F=3 system in cesium, measured through polarization spectroscopy.