Nullstein said:
This is the exactly the correct explanation for this phenomenon and it's well understood. It's just the effect of conditioning on a
Collider. I tried to explain this to DrChinese in another thread already without success. His central misunderstanding is to believe that A & D are entangled when really
they are in a perfectly uncorrelated product state. Only the conditional subensembles are entangled, but that doesn't entail any causal relationship, because conditioning on a collider generally generates fake correlations. Entanglement swapping indeed adds nothing new to the mystery of entanglement.
The experiment is performed on the entangled sub-ensemble, the other pairs are not of any interest. You never consider B & C pairs that do not arrive together within a suitably small time window. The other pairs appear equally often, separated into 4 combinations. For all intents and purposes, all of those are considered.
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Obviously, the problem with your idea is that you want it both ways... the A & D pairs are in product states to begin with, but they become entangled by your purported distillation process. Were that true, then you would be agreeing with me and be inconsistent. But I will try to work through your reasoning as best possible anyway.
As I mention, your distillation process - "entanglement swapping" or "quantum teleportation" is what everyone else calls it - doesn't have enough outcome options to match up photons with leading to perfect correlations for ultimately entangled A & D pairs. There are essentially a large (or perhaps infinite) number of angle settings at which they would need to matched for your idea to work. Your idea being that A & D happen to have identical predetermined orientations (which are reflected in their respective twins, B & C).
So let's say we have A & B entangled, and C & D entangled. We ALREADY know from Bell that the A & B (or C & D) entanglement cannot itself be explained by any local hidden variables. So basically, your idea is already failed (as you are attempting to push a local realistic explanation for entanglement swapping in which Bell's Inequality is violated).
Regardless, and still going down your path: We compare B & C, considering only those pairs in which B & C arrive together at a single polarizing beam splitter within a small time window; and are therefore indistinguishable. There can be only 4 outcomes corresponding to the four maximally entangled Bell states |Φ+>, |Ψ+>, |Ψ−>, and |Φ −>. If your idea is correct, there is no "process" occurring - since there is nothing happening when B & C interact other than to "reveal" some pre-existing correlation. But what would that pre-existing correlation be IF there are only 4 possibilities? That implies that there exist exactly 2 and only 2 different streams possible from a PDC source (since combining those 2 types you'd get 2x2=4).
That doesn't sound too crazy at first blush, but it begs the question: why do you need the compared streams to be *indistinguishable* to reveal their matching state? You could equally well run the B & C photons into *different* polarizing beam splitters such that their arrival times were within the coincidence window - just as they would be if they appeared in the same PBS. They would now be distinguishable (remember there are still only 4 outcome possibilities, as you need there to be only 2 types of PDC streams), but there would be no interaction and no swapping process. This shouldn't make any difference if your idea is correct.
A & D do NOT end up entangled, unless B & C are indistinguishable. Which is the opposite of your idea.
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The ideas you push are wrong, and it is more fully debunked in a generally accepted reference I gave in post #36. In their words:
https://arxiv.org/abs/0911.1314
"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities. Intuitively, it seems that such entanglement swapping experiments exhibit nonlocal effects even stronger than those of usual Bell tests."
"In our scenario, however, they are two separate sources S1 and S2. It it thus natural to assume that the local model assigns two different states λ1 and λ2, one to each source..." [Just as I describe above.]
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Even though the local variables λ1 and λ2 are initially independent, once conditioned on the joint measurement result of Bob they will bear enough correlations to reproduce 2 non-trivial correlations between Alice’s and Charles’s system. These correlations, however, are much weaker than those that can be established through joint measurements in quantum theory. We introduce below a (quadratic) Bell inequality that is satisfied by all bilocal correlations, but which is violated by quantum correlations." [I.e. you can't get perfect correlations from your assumptions.]
I could quote as many additional seminal papers on the subject as one would desire. None of them will agree with your analysis, and as of yet no one here has bothered to present anything remotely suitable to rebut the above references or anything I have said on the subject.
This is the Interpretations subforum and the rules are more relaxed here; but generally accepted science is still generally accepted science. The facts are: entanglement swapping is a quantum process, and it itself violates local realism. I say it is a physical process, and if you follow Bohmian Mechanics or MWI you should agree with me. I don't see how it can be viewed as OTHER than a physical process, but I would acknowledge there are plenty of other interpretations that might see things differently. But it is not a local realistic phenomena.