Hmm interesting. I may have been mistaken about the electrons only being entangled in a single direction. I thought that if you prepared a pair of electrons in state 1/sqrt(2) (|z+z-> + |z-z+>) and then measured it in y there would be no correlation, but based on: …stackexchange.com/…/intuition-for-results-of-a-m… …stackexchange.com/…/what-is-the-quantum-state-of…
if I had done the 90° rotation properly, the math works out such that the electrons would still be entangled in the new y+ basis! There is no way to only entangle them in z alone - if they are entangled in z they are also entangled in x and y. My math skills were 20 years rusty, sorry!
I still think my original proposition, that in the DCQEE under Copenhagen, an observation that collapses one photon, collapses the other photon to a sub-superposition, can be salvaged. In the second stackexchange link we are reminded that for a single electron, the superposition state 1/sqrt(2) (|y+> - |y->) is the same as |z+> state! They describe the same wavefunction psi, expressed in different basis: (y+,y-) vs. (z+,z-). When we take a single electron in superposition 1/sqrt(2) (|z+> + |z->) and measure it in z, and it collapses to, say, z+, we know that it is a pure state in z basis, but expressed in y basis it is now a superposition of 1/sqrt(2) (|y+> - |y->)! Indeed if we measure it now in y, we will get 50% y+ and 50% y-.
So in DCQEE when you collapse the first photon into a single position on the screen, the twin photon does collapse, but its basis is not expressed in terms of single positions! It’s some weird agglomeration of them. If you were to take that “pure” state and express it in terms of position basis, you would get a superposition of, say, 80% path A and 20% path B.