Do Entangled Photons React to possible Photon-Photon Collisions?

[Joseph1785]

TL;DR

The limitations of engagement and possible results of the Breit-Wheeler theory collider in relation.

Summary: The limitations of engagement and possible results of the Breit-Wheeler theory collider in relation.

*You will need to read the article for this to make sense Upon reading an article "Scientists discover how to turn light into matter after 80-year quest" I had a thought, How will entangled photons react to this? Although I know this would be incredibly hard to do, isolating two photons and managing to get one of the photons to collide with another, is it possible and if so what would happen? To tackle the question we need to do a few things, first off one need to have two entangled photons. This is a very well documented phenomenon and is rather do-able. Next, we need to isolate one of the photons, we will call him P1, so it can be observed. Now, all we need is to get P2 to participate in the "photon-photon collider" and for P2 to "create" the electrons and positrons as a result. P1 is entangled but it's partner, P2, was just turned into electrons/positrons. Will P2 do the same? Does this break any known laws/rules? Is this even FEASIBLE? I don't know but I'm sure one of you do. Are there any flaws in this I don’t see?

 

[Nugatory]

Will P2 do the same?

(I think you meant P1?)
No.
To go into more detail than that we need to talk about what entanglement is - it’s not what you’re thinking.

We have a quantum system consisting of two particles. We’re interested in some property of these particles, like say their spin along some axis (it will be either up or down along that axis). It’s one quantum system so it has one wave function, which we can write as something like $|UU\rangle$ (both particles spin-up), $|UD\rangle$ (particle 1 is spin-up, particle 2 is spin-down), and so forth. But another possible wave function is a superposition of these, something like $|UD\rangle+|DU\rangle$ which is an entangled state. This is a superposition of “particle 1 spin-up and particle 2 spin-down” and “particle 1 spin-down and participle 2 spin-up”. Any measurement of the spin of either particle will collapse the wave function to either $|UD\rangle$ or $|DU\rangle$, thereby determining the spin of the other one. That’s what entanglement is about, and it only makes sense in the context of some particular observable property (spin along some axis in this example).

Usually when people talk about entangled photons, they mean specifically polarization-entangled photons: a quantum system containing two photons and in a superposition such that collapsing the wave function determines the polarization of both.

So assuming that’s what you mean by “entangled photons”... We start with a pair of photons in a quantum state like $|HV\rangle+|VH\rangle$ where $H$ and $V$ are the two possible polarizations. One photon goes off into the photon-photon collider, interacts with another photon there and produces, and electron-positron pair. This interaction collapses the wave function of the pair, so now the other photon will definitely be either V polarized or H polarized... and that’s all the entanglement does.

 

[PeterDonis]

P1 is entangled but it's partner, P2, was just turned into electrons/positrons. Will P2 do the same?

As @Nugatory said, I think you mean, will P1 do the same? And as he said, the answer is no.

What will be the case is that the total spin of the electron-positron system that got created from P2 will be entangled with P1; the total spin of the electron-positron system "inherits" the entanglement of P2 with P1. Which means that measurements of the spins of the electron and positron will be correlated with measurements of the polarization of P1--just as measurements of the polarization of P2 would have been correlated with measurements of the polarization of P1 before P2 was put through the collider.

 

[PeterDonis]

This interaction collapses the wave function of the pair

I'm not sure that has to happen. I think all that has to happen is that the total spin of the electron-positron system inherits the entanglement of the polarization of P2 with the polarization of P1, as I said in my previous post.

 

[Nugatory]

I'm not sure that has to happen. I think all that has to happen is that the total spin of the electron-positron system inherits the entanglement of the polarization of P2 with the polarization of P1, as I said in my previous post.

I was oversimplifying (as my answer was already pushing the limits of a B-level thread) and you’re right of course.