- #106
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DrChinese said:Gee, I am not sure how much clearer they could have put it. And they come as close to the title of this thread as can be: "Photons from separated sources can be entangled - after they were detected!" I certainly get the feeling that you are going to great lengths to avoid buying a Cowboy fan a beer.
So here are the quotes, please reference again the attached diagram in Post 84. Those figures are from the Zeilinger article.
Article body:
"A seemingly paradoxical situation arises — as suggested by Peres [4] — when Alice’s Bellstate analysis is delayed long after Bob’s measurements. This seems paradoxical, because Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured. Nevertheless, quantum mechanics predicts the same correlations. Remarkably, Alice is even free to choose the kind of measurement she wants to perform on photons 1 and 2. Instead of a Bell-state measurement she could also measure the polarizations of these photons individually. Thus depending on Alice’s later measurement, Bob’s earlier results either indicate that photons 0 and 3 were entangled or photons 0 and 1 and photons 2 and 3. This means that the physical interpretation of his results depends on Alice’s later decision.
"Such a delayed-choice experiment was performed by including two 10 m optical fiber delays for both outputs of the BSA. In this case photons 1 and 2 hit the detectors delayed by about 50 ns. As shown in Fig. 3, the observed fidelity of the entanglement of photon 0 and photon 3 matches the fidelity in the non-delayed case within experimental errors. Therefore, this result indicate [sic] that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres [4]: this paradox does not arise if the correctness of quantum mechanics is firmly believed."
Figure 1: Shows diagram of setup.
"One photon from each pair is sent to Alice who subjects them to a Bell-state measurement, projecting them randomly into one of four possible entangled states. ... This procedure
projects photons 0 and 3 into a corresponding entangled state. [Bob] hands his results also to Victor, who sorts them into subsets according to Alice’s results, and checks each subset for a violation of Bell’s inequality. This will show whether photons 0 and 3 became entangled although they never interacted in the past. Interestingly, the quantum prediction for the observations does not depend on the relative space-time arrangement Alice’s and Bob’s detection events. "
Figure 3: Shows Fidelity, and Fidelity with Delayed Choice. [Note the words "delayed choice"]
"The square dots represent the fidelity for the case that Alice’s and Bob’s events are space-like separated, thus no classical information transfer between Alice and Bob can influence the results. The circular dot is the fidelity for the case, that Alice’s detections are delayed by 50 ns with respect to Bob’s detections. This means, that Alice’s measurement projects photon 0 and 3 in an entangled state, at a time after they have already been registered."
So can you point to any sentence above which makes you think that a) delayed choice version was not observed; b) entanglement did not occur; or c) the order of Alice and Bob's actions makes ANY difference to the outcome? Because it certainly seems clear to me. I don't even see in your analysis where the outcomes are different based on ordering.
Look, I am not trying to avoid anything ... but you missed the point of my argument. I am familiar with all of the quotations from the paper, and I can sketch the figures from memory, that is not the issue. What I am saying is that the entanglement and detection events are two separate parts of the BSM. To put it another way, will there be any teleportation if the fibre beam splitter in figure 2 is removed? I don't think so, because it is only by interfering inside that beam splitter that the photons 1 & 2 (and hence 0 & 3) become entangled. My entire analysis is based on that point. To put it yet another way, I am saying that I agree that detection order doesn't matter provided that the entanglement of pairs 0 & 1 and 2 & 3 still exists when 1 & 2 enter the beam-splitter. However if 0 and 3 have already been projected into definite polarization states by interacting with their detectors, then by definition, they are no longer entangled with 1 & 2, so there is nothing to teleport.
Do you somehow disagree that when one member of an entangled pair is measured, they cease to be entangled? If you do, please explain why. If you do not, please explain how the two photons with well-defined polarization states can become entangled in the specific example under consideration, that is, where 0 & 3 have been measured *before* 1 & 2 reach the fiber beam splitter. Where is the flaw in my mathematical analysis from my previous post? Please be specific. If I am wrong here, I want to know why.
Also, please don't rely on quotations from the paper, because their measurements do not address this specific case. I have absolutely no problem with the results or conclusions of that paper. My only issue is with your original example from this thread. You have not really provided any solid evidence for why you think the results of the Zeilinger paper can be extended to your example. Your vague argument about being able to "reconstruct the two-photon initial state" was far from clear, and was not supported by the reference you posted. Can you provide a more detailed explanation of what you were talking about?