A Post-Selection: Pre-existing Correlations or Action At A Distance?

[Nullstein]

1. We agree.

Apparently we don't. In your previous post you say the opposite and your current post is also in contradiction with that. You claim that the full ensemble after measurement is given by $\rho_{23}\otimes\rho_{14}$. This is provably wrong.

2. In an "event ready" variation of this experiment, somewhat similar as presented in my reference c, you can have a situation such as this (starting with the usual [1 & 2] and [3 & 4] entangled pairs):

a) Ilya receives a [2] photon and a [3] photon and performs a BSM. When a successful Psi+ BSM occurs, he sends a classical signal to Jean, who is distant.

b) Jean receives a [1] photon and a [4] photon and stores them without observing their polarization. This can occur before or after a), but the storage of these photons occurs outside the light cone of Ilya's BSM.

The BSM cannot, according to the "Pre-existing Correlations" viewpoint, change the state of either [1] photon or the [4] photon that Jean is storing. No Bell measurement is performed yet on [1] and [4].

c) Jean freely and randomly chooses a common polarization setting to measure the [1] and [4] photons.

d) Jean gets the signal from Ilya saying that the swap has been performed, indicating the stored [1] photon and [4] photon are currently entangled. Jean retrieves the [1] photon and [4] photon, and measures them at the chosen angle.

Each and every single pair will be perfectly polarization correlated for any choice of angle setting. There are no spurious correlations. You could also say there are no subensembles and no statistical considerations.
The cause is simple, a successful BSM occurred and led Ilya to press the "event ready" button (which sent the signal to Jean). The BSM remotely changes the [4] photon from being entangled with [3], to being entangled with [1]. That change is physical, and occurs faster than c.

Your reference c is a standard entanglement swapping experiment where subensembles are taken based on the BSM measurement. In entanglement swapping, entanglement appears always only in subensembles. So the argument that no conclusion about the full ensemble based on statistics of subensembles can be drawn, still holds.

 

[Nullstein]

1. I am not disputing this, never have. If there are no BSMs, then there are no swaps. So there is no [1 & 4] entanglement. None. Not in any subensemble, not in any single pair. Zero.

There are BSM's though. The state of the full ensemble after the BSM is given by equation (8.8) in Isham. Do you agree or not?

2. Nobel prize winning Zeilinger might be in contradiction with Nobel prize winning Zeilinger, I can't say. I am simply quoting from his published experimental work with other team members. I'd say that's a fair quote though, coming within a referenced paper that this thread is based on. He has plenty of other papers in his incredible body of work saying virtually the same. So it was a surprise to me when someone said he followed an information-type interpretation. Hey, from time to time, Bell hinted that he was a Bohmian. So I guess these greats also have the same troubles with interpretations as us mortals.

Well, your quote just doesn't imply what you believe it implies. Zeilinger makes a much weaker statement than you do, so he is not contradicting himself.

3. Go back to your 1. where we agree there is no entanglement if no BSM. Iff there is a BSM, then there is [1 & 4] entanglement. And it occurs remotely. Cause and effect, but without consideration of direction in time.

In 1., I explained that there is no entanglement between 1&4 in the full ensemble even after the BSM. This is a mathematical theorem and it seems like you are contradicting it. It is actually hard to tell what your claim is, since sometimes you claim to agree but then again you say something completely in disagreement with it.

 

[PeterDonis]

Entanglement has a mathematical definition that can be checked.

Yes, but which state you apply that mathematical definition to is interpretation dependent.

On a non-ensemble interpretation, where the 4-photon system for each individual run is described by its own state, the 1 & 4 photons are entangled on the individual runs, by the same mathematical definition you are using. You are dismissing that because those individual runs are part of a "subensemble", but that just emphasizes the fact that you are using an ensemble interpretation where @DrChinese is not.

 

[PeterDonis]

spooky action at a distance a la measurements on Bertleman's socks.

Measurements on Bertlmann's socks cannot show any spooky action at a distance, because such measurements cannot violate the Bell inequalities.

I haven't read the papers you referenced yet, so I don't know whether they use the Bertlmann's socks metaphor or not; but you should not be using it in this thread since it is irrelevant to what we are discussing.

 

[DrChinese]

The mathematical fact is that the full ensemble has a particular density matrix. But whether that means "no entanglement between 1 & 4" depends on how you interpret the density matrix. In the interpretation @DrChinese is adopting, entanglement is not a property of an ensemble at all, it's a property of individual quantum systems. So looking at a density matrix that averages over an ensemble of systems does not and cannot tell you whether particular individual systems in individual runs are entangled.

Exactly!

Each and every pair is initially entangled. And each and every entangled pair is maximally entangled. So there are no 3 photons that are simultaneously entangled. That a deduction from standard QM.

And for each and every entangled pair that you might choose to test, there will be perfect correlations at any angle you might choose. In other words, you know the outcome of each every single polarization pair (as identical) before you perform the measurement.

There is no statistical result to consider, other than 100%. You can't accept the math of QM, and then fail to apply MOE where there is maximal entanglement.

 

[PeterDonis]

We can post-select by interacting with 1 and 3, and infer a correlation between 1 and 4

No, that's not what's happening in the entanglement swap experiments. In those experiments we interact with 2 & 3 and pick out a particular set of runs where that interaction gives an "event ready" signal, and look at the correlation between 1 & 4 for that set of runs.

I can post-select for a pink sock on the left foot and know that the right foot in this subensemble will not have a pink sock.

Yes, but you can't produce correlations that violate the Bell inequalities this way.

Read the last paragraph of my post #9 for a better description of what happens in entanglement swapping experiments, in terms of an analogy with coin flips.

 

[Morbert]

Measurements on Bertlmann's socks cannot show any spooky action at a distance, because such measurements cannot violate the Bell inequalities.

There are crossed wires here. When I said "without invoking spooky action at a distance a la measurements on Bertleman's socks", I meant a la Bertleman's socks which also does not involve spooky action.

 

[DrChinese]

1. There are BSM's though. The state of the full ensemble after the BSM is given by equation (8.8) in Isham. Do you agree or not?

2. Well, your quote just doesn't imply what you believe it implies. Zeilinger makes a much weaker statement than you do, so he is not contradicting himself.

3. In 1., I explained that there is no entanglement between 1&4 in the full ensemble even after the BSM. This is a mathematical theorem and it seems like you are contradicting it.

1. Here is the notation for the BSM group/subset/ensemble/whatever, as originally supplied by @vanhees71 (let's stick with this since we should use this preferred format):

We have also established that the final quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$
2. The Zeilinger team says: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4." They were previously uncorrelated, and later they were correlated. Is there something ambiguous in the phrase "previously uncorrelated" that I don't understand?

3. No, the math of QM says: After a BSM, ALL successfully swapped [1 & 4] pairs are entangled and NONE of the corresponding [1 & 2] pairs are entangled. You can deduce that from the notation.

 

[Morbert]

No, that's not what's happening in the entanglement swap experiments. In those experiments we interact with 2 & 3 and pick out a particular set of runs where that interaction gives an "event ready" signal, and look at the correlation between 1 & 4 for that set of runs.

This is a typo, which I have now fixed.

 

[gentzen]

On a non-ensemble interpretation, where the 4-photon system for each individual run is described by its own state, the 1 & 4 photons are entangled on the individual runs, by the same mathematical definition you are using.

In the "standard" non-ensemble interpretation, you have to non-locally update the state upon learning new information about the state. And if you learn new information about the past, then a past state can "be updated" too ("in the past") based in new information in the present.
At least that was the opinion of Peierls.

[No self quotes or references to works allowed here, please!]

Oh wait, I am not allowed to link to my post that quoted from Peierls, “In defence of ‘measurement’”? But honestly, I don't know what should be meant by "references to works", so maybe a link to my post with quotes is still allowed after all.

 

[PeterDonis]

When I said "without invoking spooky action at a distance a la measurements on Bertleman's socks", I meant a la Bertleman's socks which also does not involve spooky action.

As I said, a "Bertlmann's socks" model cannot account for violations of the Bell inequalities. So you should not be mentioning any such model in this thread, which is talking about experiments that do show violations of the Bell inequalities. Whether or not you want to call Bell inequality violations "spooky action at a distance" or not, such violations are there in the actual experiments, so any metaphor that suggests a model that is already known to be unable to account for such violations is simply out of place in this thread.

 

[Nullstein]

Yes, but which state you apply that mathematical definition to is interpretation dependent.

No, not at all. One can apply it to all states in all interpretations. And all interpretations agree that the full ensemble is not entangled, whereas the subensembles are entangled. What is interpretation-dependent is how to interpret the entanglement of the subensembles. Some interpretations say that it is due to spooky action at a distance. Other interpretations say that it is due to bias introduced by post-selection.

On a non-ensemble interpretation, where the 4-photon system for each individual run is described by its own state, the 1 & 4 photons are entangled on the individual runs, by the same mathematical definition you are using. You are dismissing that because those individual runs are part of a "subensemble", but that just emphasizes the fact that you are using an ensemble interpretation where @DrChinese is not.

No, I'm not using an ensemble interpretation. (Not that it matters. If you agree that the post-selection interpretation of the correlations is valid in an ensemble interpretation, I'm already satisfied.)

I don't understand what you mean by entanglement here. An individual run can't be "entangled", because it is not a state and if something is not a state, one can't apply the definition of entanglement to it. But still, an individual run is part of both a subensemble and the full ensemble, which can have different entanglement properties.

 

[DrChinese]

Oh wait, I am not allowed to link to my post that quoted from Peierls, “In defence of ‘measurement’”? But honestly, I don't know what should be meant by "references to works", so maybe a link to my post with quotes is still allowed after all.

The "In Defense Of Measurement" would probably be fine if it weren't behind a paywall. But I've read a zillion papers that discuss this person's or that person's view on some point (often including their own views alongside). Most of those are neither enlightening nor rigorous, even if they are interesting.

The abstract says Bell had reservations about "collapse". Don't most people have reservations (or questions) about collapse? All I know is that whenever an irreversible measurement occurs, you find the system in a single eigenstate on some basis. Most people call that "collapse", regardless of whether they believe there is such a thing as wavefunction collapse. I do.

 

[PeterDonis]

One can apply it to all states in all interpretations.

One can mathematically apply it to any state whatever, and of course this math is independent of any interpretation.

But that is not at all the same as saying that all interpretations agree on the meaning of these mathematical operations. Consider the following mathematical facts:

(1) The math applied to the density matrix that describes what you are calling the "full ensemble" shows no entanglement between 1 & 4.

(2) The math applied to the density matrix that describes what you are calling the "subensemble" picked out by the "event ready" signal at the BSM does show entanglement between 1 & 4.

These are mathematical facts, independent of any interpretation. However, you and @DrChinese have very different interpretations of what these facts mean.

On your interpretation, fact (1) above has physical meaning: it describes the actual, physical preparation that is done at the start of the experiment. But on your interpretation, fact (2) above does not have physical meaning: it is a mathematical artifact of picking out a subensemble.

On @DrChinese's interpretation, both of these mathematical facts have physical meaning. Fact (1) physically describes the state of the 4-photon system at the start of each individual run. He is not using an ensemble interpretation, so to him the math describes individual runs, not ensembles of runs. On his interpretation, fact (2) physically describes the state of the 4-photon system for those runs in which the BSM gives an "event ready" signal. He doesn't care that this is a "subensemble", because he's not using an ensemble interpretation: on his interpretation, the BSM is a physical operation that is performed on the 4-photon state that changes it from the fact (1) state that was originally prepared, to some other state. Which other state depends on the outcome of the BSM, and the way the experiment is set up, only one BSM outcome gives an "event ready" signal, and on the runs where that signal is given, the fact (2) state is the one that the BSM produces.

 

[Morbert]

As I said, a "Bertlmann's socks" model cannot account for violations of the Bell inequalities. So you should not be mentioning any such model in this thread, which is talking about experiments that do show violations of the Bell inequalities. Whether or not you want to call Bell inequality violations "spooky action at a distance" or not, such violations are there in the actual experiments, so any metaphor that suggests a model that is already known to be unable to account for such violations is simply out of place in this thread.

My use of the model is absolutely fine and 100% appropriate in this thread, because I am discussing ways in which the intuitive reasoning of the model can be recovered in a quantum context. I am not (as you seem to think) presenting the model as accounting for violation of Bell inequalities observed in experiment.

 

[PeterDonis]

I'm not using an ensemble interpretation.

Then I fail to understand why the word "ensemble" keeps showing up in your posts. If you're not using an ensemble interpretation, then ensembles and subensembles are irrelevant. You should be interpreting the states as describing the actual, physical states of the 4-photon system on each individual run, as I do in the latter part of post #44.

 

[PeterDonis]

My use of the model is absolutely fine and 100% appropriate in this thread, because I am discussing ways in which the intuitive reasoning of the model can be recovered in a quantum context.

Sorry, but I don't buy it. The intuitive reasoning of the model is still the same reasoning that we already know cannot account for violations of the Bell inequalities. And that is sufficient to make it irrelevant to this discussion.

 

[PeterDonis]

I don't understand what you mean by entanglement here. An individual run can't be "entangled", because it is not a state

Sure it is--on a non-ensemble interpretation.

 

[DrChinese]

I don't understand what you mean by entanglement here. An individual run can't be "entangled", because it is not a state and if something is not a state, one can't apply the definition of entanglement to it.

Of course entanglement is a state, and each pair can be labeled as entangled for each and every individual run.

Where you are getting confused is whether you can prove it is entangled for a single pair. That is a completely different discussion. When you are using PDC, it is pretty easy to find the entangled pairs.

 

[gentzen]

As has been discussed in other threads on this topic, only one of those 4 Bell states for 2 & 3 is detected as an "event ready" signal from the BSM on 2 & 3. ... (Actually, in the real experiments only a small fraction of runs even meet the entry criteria for the BSM, ...)

Uups, so I misinterpreted the meaning of the "event ready" signal in my response to you in an other thread on this topic. I thought it meant that small fraction of runs even meet the entry criteria for the BSM:

Subensemble Before (Initial Preparation):

That is not right. The subensemble already was in state $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}$$ before the final observation.

What subensemble? There can't be any such subensemble in the initlal state. That's the point of the monogamy of entanglement argument.

I guess the subensemble which was selected by the final observation. If you want, you can also say that it is unclear what DrChinese means by Subensemble Before (Initial Preparation), because in a certain sense, the subensemble has not been determined yet at that point.

You can just pick the subset of runs for which the BSM measurement gives an "event ready" signal, and look at the initial state for that subset of runs.

Yes, then you are right, and the state that DrChinese gave for that (sub)ensemble was correct.

Anyway, if I follow what I wrote above:

In the "standard" non-ensemble interpretation, you have to non-locally update the state upon learning new information about the state. And if you learn new information about the past, then a past state can "be updated" too ("in the past") based in new information in the present.

then I can use that interpretation to still agree with your suggestion.

 

[DrChinese]

On @DrChinese's interpretation, both of these mathematical facts have physical meaning. Fact (1) physically describes the state of the 4-photon system at the start of each individual run. He is not using an ensemble interpretation, so to him the math describes individual runs, not ensembles of runs. On his interpretation, fact (2) physically describes the state of the 4-photon system for those runs in which the BSM gives an "event ready" signal. He doesn't care that this is a "subensemble", because he's not using an ensemble interpretation: on his interpretation, the BSM is a physical operation that is performed on the 4-photon state that changes it from the fact (1) state that was originally prepared, to some other state. Which other state depends on the outcome of the BSM, and the way the experiment is set up, only one BSM outcome gives an "event ready" signal, and on the runs where that signal is given, the fact (2) state is the one that the BSM produces.

Very well said.

What is interesting is that the experimental papers only talk about cases where a BSM occurs. And when I say BSM, of course what I really mean is: The [2] and [3] photons are NOT distinguishable, and then looking that corresponding Bell States (Psi+, Psi- etc.) ARE distinguishable. They don't really think in terms of subensembles, as they are looking for [2] and [3] photons are being indistinguishable as their universe. Much like with PDC itself: only 1 photon in maybe 10 million down converts. The photons that don't are not discussed.

If the [2] and [3] photons are indistinguishable, they will cause a swap on [1] and [4]. Although of course there are 4 different Bell States (for 2 photons), and there is approximately equal probability for each.

 

[Morbert]

The intuitive reasoning of the model is still the same reasoning that we already know cannot account for violations of the Bell inequalities.

My use of the model is absolutely fine and 100% appropriate in this thread, because I am discussing ways in which the intuitive reasoning of the model can be recovered in a quantum context. I am not (as you seem to think) presenting the model as accounting for violation of Bell inequalities observed in experiment.

There are interpretations of QM that are consistent with experiment, and understand measurements like the BSM as selecting subensembles that exhibit some property, without needing to posit some superluminal creation of this property post-BSM, in the same way that, if we measure one of Bertleman's socks, we do not need to posit a superliminal creation of the other sock to accommodate our inferences.

This does not mean, however, that QM is reducible to a Bertleman sock model of variables.

 

[Nullstein]

1. Here is the notation for the BSM group/subset/ensemble/whatever, as originally supplied by @vanhees71 (let's stick with this since we should use this preferred format):

We have also established that the final quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

You haven't established anything, you just claim it. I have established that your claim is incorrect by citing standard references, where the exact opposite is proved from the basic interpretation-independent axioms of QM.

2. The Zeilinger team says: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4." They were previously uncorrelated, and later they were correlated. Is there something ambiguous in the phrase "previously uncorrelated" that I don't understand?

No, but you are ignoring the fact that Zeilinger et al. make a much weaker statement than you do. The statement is that one can obtain an entangled subensemble by conditioning on the measurement result. Your additional claim is that something physical has happened to the 1&4 pair. There is no evidence for it and Zeilinger et al. don't imply this. In fact, Zeilinger has the exact opposite viewpoint.

3. No, the math of QM says: After a BSM, ALL successfully swapped [1 & 4] pairs are entangled and NONE of the corresponding [1 & 2] pairs are entangled. You can deduce that from the notation.

No, it doesn't. The math says that there is no entanglement in the 1&4 system even after measurement. The math says that there are entangled subensembles. Whether the entangledment arises due to spooky action or due to post-selection is a matter of interpretation and both viewpoints are viable.

 

[PeterDonis]

I have established that your claim is incorrect by citing standard references

No, you haven't. You have simply repeatedly established that you are using a different interpretation from @DrChinese.

 

[PeterDonis]

Thread closed.