Phase-measurement interferometry as a simulation of optimal quantum-state tomography

In this work we present an optical simulation of quantum tomography for state reconstruction based on projective measurements on mutually unbiased bases (MUBs-QT). A quantum state of dimension D = 2 is codified in the amplitude and phases of spatially separated beams in the arms of a Michelson interferometer. The quantum tomography is performed by introducing different displacements in one of the arms of the interferometer and recording the interferograms. We show that in this case the MUBs-QT is equivalent to obtain the set of measurements to extract information from the amplitude and phase of a wavefront using the four step phase shift interferometry.