Realistic interpretation of QM

[gentzen]

Do you agree that the statistics of the A&D system is fully described by its reduced density matrix? Do you agree that the local operations at B&C don't change the reduced density matrix of A&D and therefore don't change the statistics of A&D? If you answer yes to these questions, then the full ensemble of A&D (before or after, it doesn't matter) already contains all the subensembles

so far I agree

and they only need to be singled out by post-selection. Do you agree with that as well? Do you agree that singling out a sublist of a full list of already performed measurements is a perfectly classical thing to do?

I don't see why singling out a sublist should be a perfectly classical thing to do. And I see it even less when it comes to implementing a physical process that will do that singling out. (Also note that for me, postselection is a typically quantum thing. A typically classical thing would be statistics caused by an preexisting but unknown state.)

In that case, we're now in a completely classical statistical situation and the only thing left to understand is that singling out such a sublist may introduce a bias (new correlations) in the statistics of the resulting subensemble.

Here I agree that the change in statistics caused by forming sublists can be analysed as a completely classical statistical situation. But I disagree that this would be the non-trivial part which needs a reference to back it up.

But overall, I agree that this constitutes a serious attempt "to bring forward a convincing argument".

If the only thing you agree with in vanhees' post is that the subensembles are entangled, then you still haven't satisfied @gentzen's demand to clarify your stance on the entanglement of the full ensemble of the A&D system (before and after measurement).

He explicitly wrote: "I think vanhees71 says it nicely and I agree with everything he says." So even if I would have made an explicit demand to clarify his stance, that demand would now be satisfied.

 

[Nullstein]

I don't see why singling out a sublist should be a perfectly classical thing to do.

So suppose you have a list of ~1000 measurement results, written on a piece of paper and your task is to strike through ~750 of them based on the rule that everything should be removed unless e.g. $B=1$ and $C=-1$, what is quantum about this task? You literally just remove lines from a macroscopic piece of paper by striking them through with a pencil.

And I see it even less when it comes to implementing a physical process that will do that singling out.

But it's not done by a physical process. It's done manually or by a classical computer (which strictly speaking can of course also be argued to be a physical process, albeit a very classical one and I don't think that is what you meant to say here?).

He explicitly wrote: "I think vanhees71 says it nicely and I agree with everything he says." So even if I would have made an explicit demand to clarify his stance, that demand would now be satisfied.

But in the very next post, he contradicted vanhees again, so it became unclear again, what his stance is, at least to me. He claimed that it is impossible to have it both ways: The subensembles are entangled and the full ensemble is non-entangled. Yet, vanhees said the exact opposite and it is indeed possible to have it both ways. So does he believe that the full ensemble of A&D is entangled or non-entangled? From the claim that it is impossible to have it both ways, taken together with his agreement with the statement that the subensembles are entangled, I would normally conclude that he believes that the full ensemble is entangled as well, which is in direct contradiction to vanhees (whom he claimed to agree with) and accepted mainstream science. If it is clear to you what his stance is, could you light me up?

 

[Nullstein]

Let me try to explain it in a different way:
You may be intruiged by the fact that the protocol includes a measurement at B&C. But really, you don't have to do this. Suppose you start with the two pairs A&B, C&D and don't perform a measurement at B&C. You do nothing there. You just measure A&D as before and compile a list of ~1000 results. Then you select ~250 of them just by chance, e.g. by coinflips. There is a tiny chance that you make a correct choice and this sublist of ~250 measurements result will be perfectly entangled, even though you have done precisely nothing to the photons at B&C. So it's really just the singling out of the sublist that introduces the entanglement in A&D and not the measurement at B&C. The operation at B&C does not in any way affect the state of A&D. It does not cause the entanglement of A&D.

The reason for performing the measurement at B&C is to consistently choose the right sublist and not having to rely on chance. There is no physical process occurring to A&D that would entangle them. We know this because $\rho_{AD,after} = \rho_{AD,before}$, so the "before"-state statistically already contains the entangled subensembles, even if we don't perform an operation at B&C.

The fact that $\rho_{AD,after} = \rho_{AD,before}$ proves that it is not the measurement at B&C that causes the entanglement of subensembles of A&D. But then why is it that a measurement at B&C is so helpful for chosing a correct sublist? That's because A is entangled with B and D is entangled with C. So the experimenter at B&C has access to the information which sublist will be the correct one, even though A&D may be far away. He just needs to devise a smart way to extract it and of course he is allowed to perform quantum operations in order to do that. But it is essential to understand that these operations do not affect A&D in any way and in particular don't cause any entanglement between A&D. That is excluded by the no-communication theorem.

 

[DrChinese]

1. And that is absolutely correct and also what vanhees said.

2. In fact it is both true. The subensembles of A&D are entangled and the full ensemble of A&D is not entangled, even after measurement. I can definitely have it both ways, because both propositions are true.

3. It would be nice if you could just complete the following two sentences:
a. The full ensemble of the A&D subsystem before measurement is __________. (entangled / not entangled)
b. The full ensemble of the A&D subsystem after measurement is __________. (entangled / not entangled)
Can you do that for me and @gentzen? Because from your posts I really can't extract what your stance is.

1. vanhees71: "In each of the four subensembles, selected by (projective) measurements on photons B&C, photons A&D are entangled. They are not entangled in the full ensemble. "

Nullstein: "The full ensemble of A&D is not entangled even after the measurement at B&C."2. I will leave your odd statement to speak for itself, just adding that I keep saying you want it both ways.3. I have stated this many a time above:
a. The full ensemble of the A&D subsystem before measurement is not entangled.
b. The SUB ensembles of the A&D subsystem after the PROJECTIVE measurement are entangled in a Bell state, of which there are 4 possibilities.

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I think one problem we are having in this discussion is that what you call a full ensemble is not the same thing is what everyone else calls it. When any Bell test is performed, there is a requirement that there be an element of indistinguishability. That is normally performed by requiring the arrival times of 2 photons to occur within a small time window. In our swapping case, that means the B & C photons arrive within that window. The "full" ensemble includes B & C pairs that arrive too far apart to be considered indistinguishable. (Note that it does not matter whether we actually know which is B and which is C.) The B & C pairs that arrive too far apart definitely do NOT lead to entangled A & D pairs (because B & C were distinguishable). The full A & D ensemble therefore consists of pairs that are definitely not entangled, as well as pairs that are definitely entangled (in principle, and not considering noise) depending on whether their B & C counterparts are distinguishable or not.

The next issue is the 4 Bell states that are possible outcomes when entanglement occurs. They are |Ψ+>, |Ψ−>, |Φ+>, and |Φ −>. Some entanglement swapping experiments identify all 4 of these sub-ensembles, and some identify only a single one. Regardless, you must know which type of entanglement is associated with each A & D pair. If you are ignoring one or more of the 4 Bell state ensembles, that is not a problem for the validity of the experiment. It just means a smaller sample size. For example, see https://arxiv.org/abs/quant-ph/0201134 and note that the quote below has been label-adjusted to match the example we are discussing

"We stress that photons A and D will be perfectly entangled for any result of the BSM [Bell-state measurement]... But it is certainly necessary ... to communicate to the Bell-state measurement result. This will enable ... sorting of data into four subsets, each one representing the results for one of the four maximally entangled Bell-states. ... In our experiment, we were restricted to only identifying the state |Ψ−> due to technical reasons. This reduction of the teleportation efficiency to 25% does not influence the fidelity."

Any sub-ensemble of A & D pairs that are identified as meeting a) the B & C indistinguishable requirement; and b) identified as being projected to the one or more of the desired Bell states; WILL be entangled.

Those sub-ensembles obviously cannot be entangled because they just happen to arrive at the same time - they are from independent source (in some of the experiments). If that was the trigger: then there would be no indistinguishability requirement and you would not need to allow the A & B biphoton system to interact with the C & D biphoton system. You would simply check the arrival times of the B & C photons, which can be done without allowing the 2 original biphoton systems to interact.

Again, the point of all this is that entanglement swapping creates new entangled A & D photon pairs, and the preparation process cannot be considered local since A & D are far apart when the swapping operation occurs as a result of a Bell State Measurement on B & C. Of course, another way of looking at it is to say that the A & B biphoton system (which has nonlocal extent) interacts locally with the C & D biphoton system (which also has nonlocal extent). That's a matter of interpretation.

 

[PeterDonis]

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