How Would Afshar's Experiment Affect Entanglement?

[Erik Ayer]

TL;DR

If one of the two beams from non-colinear SPDC were sent through Afshar's experiment, would momentum, path, and/or polarization entanglement be broken?

Afshar's experiment (https://en.wikipedia.org/wiki/Afshar_experiment) sent a light beam through a double-slit to get interference, put wires in the places where there were dark fringes, then refocused the light with a lens get "image" the two slits. I'm wondering what entanglements would break if one beam from an entangled source were sent through Afshar's experiment. To keep this slightly simple, assume the two beams with entangled photons are from type 2 SPDC and are not colinear - they two beams go in different directions.

What I would expect is that momentum entanglement would be broken when the beam went through the slits and diffracted. However, I wonder whether it could be preserved if, instead of slit, the beam were split with a regular old (non-polarizing) beam splitter and the two sub-beams made to overlap and interfere with a lens. My guess would be that path entanglement would survive since a photon going through the left slit would end up in the left image and one going through the right slit would end up in the right image after the lens. Polarization entanglement would survive since Afshar's experiment does nothing to measure or collapse the polarization state of superposition.

 

[Strilanc]

The dark spots that you'd put the wires in will not be present when the photon is entangled with another photon. You won't be able to find a spot where a detector never clicks. Ignoring that and putting the wires in the usual place would be equivalent to measuring the photon in the "left slit + right slit vs left slit - right slit" basis (or something of that nature), downgrading the entanglement between the two photons into correlation.

 

[Erik Ayer]

Thank you for your response! If I understand correctly, the momentum entanglement would be destroyed. I'm not sure about path entanglement of whether it even makes sense to ask about that. However, would polarization entanglement remain intact? It seems like it should.