State estimation: A comparison between direct state measurement and tomography

We compare direct state measurement (DSM, or weak state tomography) to conventional state reconstruction (tomography) through accurate Monte Carlo simulations. We find that DSM is much less precise than tomography, but it is surprisingly robust to its inherent bias, which introduces an unavoidable error in the reconstruction. In addition to studying DSM and proposing a method to estimate such bias from the experimental data, we show that the number of DSM measurements can be optimized and that the dimensionality of the DSM pointer is irrelevant: Both finite- and infinite-dimensional pointers provide comparable reconstructions.