State estimation: direct state measurement vs. tomography

We compare direct state measurement (DST or weak state tomography) to conventional state reconstruction (tomography) through accurate Monte-Carlo simulations. We show that DST is surprisingly robust to its inherent bias. We propose a method to estimate such bias (which introduces an unavoidable error in the reconstruction) from the experimental data. As expected we find that DST is much less precise than tomography. We consider both finite and infinite-dimensional states of the DST pointer, showing that they provide comparable reconstructions.