I recall reading that if you put a parallel polarizing filter over one slit and a perpendicularly polarizing filter over the other slit, and send a singe photon to the slits, then there is no interference pattern produced beyond the slits. The explanation was that the filters provided a "which-way" tagging of the photon and so, if that information is known, there can be no interference because the photon could only have gone through one slit. I think this view also implies wave function collapse at the slits
Suppose the photon is in a pure state before reaching the slits. I think another explanation might be:
one emergent wave is tensor multiplied by one eigenstate of polarization and the other emergent wave is tensor multiplied by a different eigenstate of polarization.
When the two tensor products are added, we get a state vector (representing the joint polarization and position states) where each state of that state vector is described by a single wave.
Therefore, when probabilities are calculated, there is no cross-term and no interference. Further, the polarization can be reversed by a simple matrix multiplication of the state vector of the photon. (Note, the photon remains in a pure state, after its wave function passes through the slits)
So, in this interpretation, there are no interference patterns, but the wave goes through both slits (without wave function collapse at the slits), unlike the information interpretation, where it goes through only one as a particle.
What do you think?