Fig. 2: Simplified experimental setup showing the Mach-Zehnder interferometer (MZI) with pre and post-selection.
The angle of the post-selection Half-Wave Plate (HWP) is kept at zero degrees to get the desired post-selection \(\left\vert \phi \right\rangle\). In arm B, the apparatus to measure the σ1 polarization component is inserted, which displaces the beam along the horizontal (along X). The glass plate (GP) in arm A makes the beam shift vertically (along Y). A 50:50 beam splitter placed after the post-selecting Polarizing Beam Splitter (PBS) causes the photons to randomly make their way to either of the two multi-mode fibers (MMF). One of the fibers is moved along X to generate the horizontal profile of the beam after the beam passes through a cylindrical lens that compresses the vertical transverse profile. The other MMF is moved along Y to generate the vertical profile of the beam after the horizontal transverse profile of the beam is compressed using another cylindrical lens. The two weak interactions in the respective arms occur at the same time and no experimental setting is changed between pre- and post-selection during the data acquisition. The coincidence measurement ensures that there is almost always a single photon within the interferometer interacting with the two operators (\(\widehat{X}\) and \(\widehat{Y}\)) in the two respective arms of the interferometer simultaneously.
