Double slit experiment setup

Question

This is a better form of a previous question I asked: Double slit experimental procedure

Basically, I want to know what constitutes a measurement of which slit a particle goes through in the double slit experiment. For the following three setups:

1. Two slits.
2. Two slits with devices that assign the particles perpendicular spins.
3. Two slits with devices that assign the particles perpendicular spins, and where the screen can tell the spin of the electron.

In the first, we have interference. In the third, we have no interference because we have measured which slit the electron passed through. In the second, is there interference or no interference?

Answer 1

Basically, I want to know what constitutes a measurement of which slit a particle goes through in the double slit experiment

Simple: whatever setup you use, if that setup can give you the which-way information, it is a measurement and you will not get interferences. If the setup is useless, you will get interferences. The details have no importance.

So your second setup is not a measurement if you do nothing with the spin tags. If you use them to recover the which-way info, then it is a measurement.

Why is it so simple? Because the fundamental idea is that any slit-observing device must by definition couple with the particle (else it cannot detect it). This means particle and observing device gets entangled; the superposition of trajectories is now linked to the superposition of the device yes/no states. In other words, the device yes/no states interfere together, along with the trajectories.

Using the device to get the which-way information means measuring it in a specific yes or no state. But the entanglement is such that when the device states do not interfere any more, the particle paths do not interfere either. That's all there is to it, and there is no way to cheat with this, whatever detection trick you may come up with.