From what I understand, wave function collapse occurs when a photon/wave/particle/whatevertheheckitis which was previously in a superposition of states, collapses to one state. Now, in a double slit experiment with single photons the photons could either pass through slit A or B. Now, once one figures out which path the photon takes, does this not necessarily collapse the wave function because the path which was previously in a superposition of two different states, collapses to one of the alternatives? I know that in the quantum eraser experiment the wave function is supposedly undisturbed, but if my reasoning is correct than during the experiment the wave function collapses. Am I right or do I have a misconception about what wave function collapse actually is?
Wave function collapse is the postulated process which occurs when a quantum system described by a superposition of states upon interaction with a classical system collapses to a single state.
Now the quantum eraser experiment has three parts to it
A photon is sent through an apparatus which does parametric down conversion which converts it into a pair of entangled photons. We only know that the two photons are entangled but nothing more about them. One of the photons is sent to a detector circuit while the other is sent to a YDSE apparatus where we see the expected interference pattern.
A clockwise circular polarizer is placed in front of one of the slits and an anticlockwise polarizer in front of another one. Now the first photon which was already sent off to the first detector is measured for its circular polarization. So we can know that through which slit the second photon passed depending on whether the photon detected at the first detector was of which polarized state. Now what happens is that since the measurement of the path takes place therefore the interference pattern is destroyed.
The path of the first photon is intersected with a linear polarizer due to which the circular polarizations are decomposed into linear states with equal probability of both polarizations. Now again an interference pattern appears.
This is how a quantum eraser works. The wavefunction collapse occurs when the path of photon is known, if it is not known then the interference proceeds as usual.
I will address this part:
Am I right or do I have a misconception about what wave function collapse actually is?
IMO it is simpler to think in terms of wavefunctions as solutions of differential equations whose complex conjugate squared gives the probability of finding a particle at (x,y,z) at time t. These solutions depend on the boundary conditions of the problem. "Collapse" is a short hand way of saying "a specific instance has been measured in the probability distribution" . Before, everything was "in potentia", after, a new solution with the new boundary conditions is necessary to describe the system.
Every time a detector or an element is entered in the experimental setup , a different solution appears, for example polarizers at slits, or on he way. In my view the experiment you refer to analyses the way the probability of scatter is built up.
Thinking of it mathematically, imo it is not surprising that a solution composed of sinusoidal functions will give interference functions, and also that affecting the phases of these functions ( as one does with the circular polarizer) can easily destroy interference patterns.