327278.fig.009
Figure 9: Action of a lens in a dual-slit setup with different polarization filters ( 𝑅 and 𝐿 ) at the slits—slits 1 and 2 create a two-slit image 1 and 2 , denoted are the focal plane of the lens 𝑓 = 2 . 2 5  m, the image plane of the lens 2 𝑓 . Plotted are the probability density functions for each slit separately ( 𝑅 in red and 𝐿 in blue) at the level of the optical axis ( 𝑦 = 0 ) for photon with 𝜆 = 6 5 0  nm passing through square slits with side of 250 μm separated by distance of 2 mm. There is perfect which-way information due to entanglement of photon polarization with photon path, and there is no interference pattern at the focal plane of the lens. The two different probability density functions ( 𝑅 in red and 𝐿 in blue) can be separated my simultaneous measurement of the photon polarization, and this is in sharp contrast with the coherent setup, where we do not have means to distinguish the photon history after the interference has occurred.