Well, the simplest way to "monitor" it is to just block one of the slits. Then you definitely know which slit photons that hit the screen went through! Alternat

Well, the simplest way to "monitor" it is to just block one of the slits. Then you definitely know which slit photons that hit the screen went through! Alternatives include: - Marking the photon itself (e.g. by rotating its polarization with a waveplate). - Placing a crystal that does spontaneous parametric down-conversion after one of the slits. This splits the photon into two photons. Aim the secondary photon at a detector. Detector clicks -> went through that slit. No click -> went through other slit. But this will also mark the photon itself with a change in frequency, so really should do it to both slits. - Having a magical device that stores a bit and toggles it anytime a photon passes through a piece of glass. Place the magical toggle-glass over one of the slits. Anything that can distinguish the case where a photon goes through the left slit from the case where a photon went through right slit will work fine.