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PeterDonis
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@DrChinese has referenced quite a few papers. Which one?Morbert said:Fig 2 from @DrChinese 's paper
@DrChinese has referenced quite a few papers. Which one?Morbert said:Fig 2 from @DrChinese 's paper
https://arxiv.org/pdf/1209.4191.pdfPeterDonis said:@DrChinese has referenced quite a few papers. Which one?
Ok. In that paper the state that is produced is, as I described before, a product state of two entangled photon pairs. (In equation 3 of the paper the state before the projection operation on photons 2 & 3 is given, but the following text makes it clear that after the projection operation, you simply have one of the four Bell states given in equation 3, and each of those is as I described.)Morbert said:
A. Neumaier said:I. So we have an entangled 4-photon state in the standard meaning, a tetraphoton, but not an entangled 2-photon state, no biphoton. The paper just shows that certain tetraphotons measured at different times produce the same correlations as a biphoton in a Bell state, and tries to sell it as ''temporal entanglement''.
II. But they don't substantiate this claim, and indeed, the claim is meaningless.
A. Neumaier said:The paper just shows that certain tetraphotons measured at different times produce the same correlations as a biphoton in a Bell state, and tries to sell it as ''temporal entanglement''.
Sorry, no. See my post #91, which explains why not. Arnold misread (or misinterpreted) something amongst the many posts. It would be easy for anyone to do.mattt said:This. In a nutshell.
Yes, I agree. What I'm still not sure about is how the state they do use, which is, as you say, a product state of two biphotons (the entanglement swap just changes which photons are in each biphoton), is produced by the apparatus that is described. The paper that describes the theoretical background, at least in a little bit of detail, only talks about how the GHZ state is produced. The paper that you referenced that describes the entanglement swapping, and uses the two-biphoton states (with similar temporal markings to the 4-photon GHZ states in the other paper), does not describe how those two-biphoton states are produced by the apparatus, and it's not clear to me from the description in the first paper (the GHZ state paper) how pair-of-biphoton states could be produced. Possibly there are other papers (which would hopefully be somewhere in the references in those two papers) that go into more detail about the latter; but I haven't seen any yet.DrChinese said:Entanglement swapping protocols don't use 4-photon GHZ entanglement
The 2 biphoton (2 photon entangled system, i.e. an entangled photon pair) Product state (N=2x2) used for the initial portion of the entanglement swapping can be produced through a number of interesting and innovative methods. Here are a few, including reference links:PeterDonis said:Yes, I agree. What I'm still not sure about is how the state they do use, which is, as you say, a product state of two biphotons (the entanglement swap just changes which photons are in each biphoton), is produced by the apparatus that is described. The paper that describes the theoretical background, at least in a little bit of detail, only talks about how the GHZ state is produced. The paper that you referenced that describes the entanglement swapping, and uses the two-biphoton states (with similar temporal markings to the 4-photon GHZ states in the other paper), does not describe how those two-biphoton states are produced by the apparatus, and it's not clear to me from the description in the first paper (the GHZ state paper) how pair-of-biphoton states could be produced. Possibly there are other papers (which would hopefully be somewhere in the references in those two papers) that go into more detail about the latter; but I haven't seen any yet.
I'm not asking about how biphoton states are produced experimentally. I already know there are multiple ways of doing that.DrChinese said:The 2 biphoton (2 photon entangled system, i.e. an entangled photon pair) Product state (N=2x2) used for the initial portion of the entanglement swapping can be produced through a number of interesting and innovative methods.
1. Well, you said (so I answered): "The paper that you referenced that describes the entanglement swapping, and uses the two-biphoton states (with similar temporal markings to the 4-photon GHZ states in the other paper), does not describe how those two-biphoton states are produced by the apparatus..." So I provided 5 examples with references. Note that none of these produce 4-photon GHZ states. I think that you and several others like the theory presented in a reference @Morbert provided in post #83. But that is a different state than the 2 biphotons in a Product State - as I think you acknowledge.2. Here is what I believe is the mathematical representation you seek, which is presented verbatim in italics and in context without interruption from several papers:PeterDonis said:1. I'm not asking about how biphoton states are produced experimentally. I already know there are multiple ways of doing that.
2I am asking about how products of two two-photon entangled Bell states are produced mathematically using a theory that, as far as I can tell, only explains how the apparatus described in both the entanglement swapping paper you referenced and the "temporal mode" paper that @Morbert referenced (which describes the theory, though not in very great detail) can produce 4-photon GHZ states.
You provided 5 references that describe experiments. That's not what I'm asking for.DrChinese said:I provided 5 examples with references. Note that none of these produce 4-photon GHZ states.
I'll take a look.DrChinese said:Here is what I believe is the mathematical representation you seek
1. They say exactly the opposite, using nearly identical wording as you: "When the two photons of time τ (photons 2 and 3) are projected onto any Bell state, the first and last photons (1 and 4) collapse also into the same state and entanglement is swapped. The first and last photons, that did not share between them any correlations, become entangled."mattt said:1. What I mean is that in the case where biphoton1,2 is created and photon1 is measured (and destroyed) before (for all possible reference frames) biphoton3,4 is created, there can be no biphoton1,4 Bell State (or any biphoton1,4 state).
2. I must conclude that you (and possibly the authors of that paper) are using these English words with a different meaning than the usual mathematical meaning.
Ok, I took a look. Here's the problem. From the 2002 paper, p. 5:PeterDonis said:I'll take a look.
Morbert said:The paper @DrChinese cites, cites this one in turn. From the paper...
I see your dilemma and acknowledge your points. Unfortunately I am not the person to bridge the published papers to your type of analysis. Without in any way taking away from your approach, I will simply point out your methodology/approach does not appear in the hundreds of papers I have read on the subject. Instead, the presentation is nearly identical in papers written in the 1999 to present time frame.PeterDonis said:Ok, I took a look. Here's the problem. From the 2002 paper, p. 5:
"A seemingly paradoxical situation arises — as suggested by Peres [4] — when Alice’s Bell-state 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."
a. My question is: how does QM predict the same correlations when the photons never coexist?
The way I did it when I did the math using the Schrodinger equation in a previous thread, there are no Bell states with photons 1 & 4. Ever. Anywhere. So that analysis, while it certainly supports the claim that QM predicts the same correlations, does not support the claim that it does so by means of Bell states with photons 1 & 4--because there are no such states anywhere in the analysis. (And you have already agreed that, if photons 1 & 4 never coexist, there is no time at which such a Bell state exists.)
b. The 2002 paper does not give any mathematical analysis to back up the claim I quoted above. So I have no way of knowing why they think that claim is true. Is it just because the experiments show the same correlations? Or is it because someone has actually done a mathematical analysis, not the same as the one I did, that does involve a Bell state with photons 1 & 4 even though they never coexist? I don't mean just writing down such a Bell state; I mean showing how such a Bell state can arise from the dynamics even though photons 1 & 4 never coexist.
c. The other paper, from 2012, does a very short mathematical operation to obtain such a Bell state: it takes the state in equation (2) and rearranges it, applying a time delay to photons 2 & 4 and algebraically refactoring, to obtain equation (3), which is an entangled superposition of the 4 possible "double biphoton" states for photons 1 & 4, and photons 2 & 3. Each photon 1 & 4 state in that superposition is a Bell State. (In actual experiments, as you have said, only 1 or at most 2 of these can actually be distinguished after all measurements are made. But that's not important for what we're discussing here.)
d. Perhaps the underlying assumption here is that standard NRQM, where you use the Schrodinger equation and you have a state of the system that evolves in time, is simply inapplicable to these types of experiments. But if that is the case, I would certainly like to see somebody justify that assumption and explain what should be put in its place.
Experimentally, yes, I agree. It's the theoretical basis that I'm not clear on--but that probably means I need to do more digging into the literature. In my copious free time.DrChinese said:The answer is that QM is not only quantum nonlocal (our agreed upon terminology), it is also quantum non-spatiotemporal.
I believe the short answer to this is "decoherence", but while the ordinary QM picture of this seems to me to be fairly straightforward, I'm not sure how the picture changes in QFT.DrChinese said:I am hoping that we can return to the discussion of Measurement in QM/QFT. What is it? Is it physical? When does it occur? What triggers it? Where does it occur?
Well, the theoretical background that I'm still not clear on is not irrelevant, since any interpretation (and this thread is in the interpretations subforum) has to rely on the theoretical background at least to some extent. To the extent that interpretations can ignore the details and simply rely on the experimentally observed correlations, yes, they would not need the theoretical details I have been asking for. The question is to what extent that is actually true.DrChinese said:I certainly hope that the cited experiments co-authored by a Nobel prize winner (and others equally well-regarded) can be used for discussion purposes without further debate.
PeterDonis said:Perhaps the underlying assumption here is that standard NRQM, where you use the Schrodinger equation and you have a state of the system that evolves in time, is simply inapplicable to these types of experiments. But if that is the case, I would certainly like to see somebody justify that assumption and explain what should be put in its place.
Do I guess correctly that Peter Donis initially did his analysis when you wanted to know how that stuff works in MWI? In that case, one explanation for the "disconnect" might be that the theoretical analysis in the papers implicitly relied on the Copenhagen interpretation, especially on the "update" of the wavefunction when new knowledge becomes available. From a MWI perspective that considers the wavefunction as something physically objective, this could feel like an invalid or incomplete analysis.DrChinese said:I see your dilemma and acknowledge your points. Unfortunately I am not the person to bridge the published papers to your type of analysis. Without in any way taking away from your approach, I will simply point out your methodology/approach does not appear in the hundreds of papers I have read on the subject. Instead, the presentation is nearly identical in papers written in the 1999 to present time frame.
To give an example: @gentzen has just commented that various papers that have been referenced appear to be using a more or less Copenhagen-type interpretation. With an interpretation like that, as @gentzen says, since the wave function is not claimed to be physically real, I think it would be perfectly fine to say, look, we know the correlations between 1 & 4 are the same regardless of the time ordering or whether those two photons ever even coexist. So it seems fine to use the same math to make the predictions in all these cases. We're not claiming that there is an actual physically real Bell state with photons 1 & 4 when they never coexist. We're just saying the Bell state is the math we are using to make predictions, and that math works.PeterDonis said:To the extent that interpretations can ignore the details and simply rely on the experimentally observed correlations, yes, they would not need the theoretical details I have been asking for. The question is to what extent that is actually true.
You do. It was in the "Is the MWI local?" thread, which was fairly recent. I did the analysis to illustrate that the MWI does give an explanation for the correlations, but I agreed with @DrChinese that its explanation is not local, because of the nonlocality of the wave function.gentzen said:Do I guess correctly that Peter Donis initially did his analysis when you wanted to know how that stuff works in MWI?
That would be one way for the MWI to handle this, yes. But note that in this case there is no Bell state for photons 1 & 4. The correlations would be accounted for by an entanglement between photon 4 and the "detector environment" degrees of freedom associated with the photon 1 measurement. (In fact this is more or less what I did in the analysis in the previous thread that I have been referring to.)Morbert said:If we adopt a MWI interpretation of NRQM with some presentist account of time, then presumably the swap will not act on the "1,2" and "3,4" biphoton systems, but rather the the "3,4" biphoton system and the "detector environment, 2" system (in the sense that these are the subsystems at time ##\tau##, just before the BSM).
This produces the entangled 4-photon GHZ state (2) of arXiv:1204.1997 that I was referring to as a tetrastate.DrChinese said:I. Sorry, perhaps either I (most likely) or the authors of the paper were not clear. There is an N=4 photon state, but there is no tetraphoton as you mention.
b. Execute Swap: Photons 2 & 3 are allowed to overlap such that their identities become indistinguishable. You could also say that biphotons (1 & 2) and (3 & 4) are allowed to overlap.
Yes, indeed. They showed that a particular measurement scheme applied to the entangled 4-photon state (whather a GHZ state or a product of two Bell states does not matter) with measurement at two different times produced the same statistics as a Bell state would have done.DrChinese said:c. Final Product state: |φ+/-14> |φ+/-23>II. The paper follows standard QM predictive methods, using quantum theory (that measurement order in entanglement swaps is irrelevant to the observed statistics) that was published at least 25 years ago. Their specific hypothesis was that measuring Photon 1 before the swap (BSM) would lead to predicted violations of Bell-type inequalities just the same as if they had measured Photon 1 after the swap. That hypothesis was substantiated, yet another confirmation of quantum mechanics - and to nobody's surprise.
There is no dispute about that. But publication of a paper in a peer reviewed journal is no guarantee for the correctness of every statement of its content.DrChinese said:It was published in Physical Review Letters 110, 210403; 22 May 2013. Obviously it passed peer review.
The very definition of entanglement contradicts the existence of temporally entangled photons. Entanglement requires a state in the Schrödinger picture belonging to the Hilbert space in question, and such a state always means a state at a fixed time.DrChinese said:Perhaps you are aware of published work that contradicts this result.
I only evaluate as meaningless the interpretation of their results as having created temporally entangled photons.DrChinese said:So I question your evaluation of their results as "meaningless".
The pattern is clear: They measured multiphoton states at different times and obtained a statistics identical with that of measuring a Bell state. In no case, they produced a temporally entangled state, since the latter is a thing that cannot be consistently defined.DrChinese said:To summarize the line of research on the nature of measurements in entanglement swapping, which was the reason I posted in this thread to begin with:
At this time, there has been experimental verification (references below from 2002 to 2012) of the following:
Hopefully, the pattern is clear: the same results are obtained, regardless of measurement order.
- Basic Entanglement Swap with Bell State Measurement (photons 2 & 3) performed prior to observation of entanglement between (photons 1 & 4). See Zeilinger et al, etc.
- Entanglement Swap with fully independent sources with Bell State Measurement (photons 2 & 3) performed prior to observation of entanglement between (photons 1 & 4). See Zeilinger et al, etc.
- Remote (photons 1 & 4 outside each others' light cone) Entanglement Swap with Bell State Measurement (photons 2 & 3) performed prior to observation of entanglement between (photons 1 & 4). See Gisin et al, etc.
- Delayed Choice Entanglement Swap with Bell State Measurement (photons 2 & 3) performed subsequent to observation of entanglement between (photons 1 & 4). See Ma et al, etc.
- Temporal Entanglement Swap with Bell State Measurement (photons 2 & 3) performed prior to observation of photon 4 but subsequent to observation of photon 4. See Eisenberg et al.
- Failure of Temporal Entanglement Swap with Bell State Measurement (photons 2 & 3) performed without indistinguishability** of photons 2 & 3, prior to observation of photon 4 but subsequent to observation of photon 4. See Eisenberg et al.
This has nothing to do with relativistic or not. The Hilbert spaces in question are finite-dimensional, so no field theory is involved.DrChinese said:I am not aware of any aspects of relativistic QFT that would add to this discussion or lead to any predictions contrary to garden variety QM.
With the exception that he is precise about the implications. The abstract says:DrChinese said:The first application of delayed choice to entanglement swapping that I am aware of is "Delayed choice for entanglement swapping" (Peres, 1999). His analysis of Bell states looks almost identical to those I have presented in various posts.
Note the subjunctive: The claim is only identical behavior of the statistics, not the creation of a meaningless temporally entangled state!Asher Peres said:each subset behaves as if it consisted of entangled pairs of distant particles, that have never communicated in the past, even indirectly via other particles.
It seems that this is the paper that coined the notion of ''entangled pair of photons that have never coexisted'', since they state thatDrChinese said:From HERE (my primary reference
But they do not give any definition of the meaning of the new concept. Thus it must be inferred by reading between the lines. Clearly it means no more than pairs of photons that reproduce the statistics of entangled photons, in the above as-if sense of Peres.Megidish et al said:Previous demonstrations [...] entangled photons that were separated spatially, but not temporally, i.e., all the photons that were entangled, existed and were measured at the same time.
Who of the authors of your primary source is a Nobel prize winner? Which year?DrChinese said:the cited experiments co-authored by a Nobel prize winner
I still have no idea how you are able to cover so much ground... I am thinking vampire...PeterDonis said:Experimentally, yes, I agree. It's the theoretical basis that I'm not clear on--but that probably means I need to do more digging into the literature. In my copious free time.
1. I agree with everything you say about https://arxiv.org/pdf/1204.1997.pdf , "A Resource Efficient Source of Multi-photon Polarization Entanglement". These are various GHZ states which do not produce pairs of biphotons. I believe @Morbert provided this for us to have a better understanding of the reference I have been using as to the underlying physical arrangement. Five of the authors are the same in both papers. It turns out the apparatus in the earlier paper can be modified to achieve the setup for the later paper.A. Neumaier said:1. This produces the entangled 4-photon GHZ state (2) of arXiv:1204.1997 that I was referring to as a tetrastate.
Yes, indeed. They showed that a particular measurement scheme applied to the entangled 4-photon state (whather a GHZ state or a product of two Bell states does not matter) with measurement at two different times produced the same statistics as a Bell state would have done.
But it didn't produce a Bell-state! Instead the first measurement reduced the number of particles, and the second reduced it again. A Bell state never appeared, and the authors of arXiv:1204.1997 never claimed that.
The authors claimed (and achieved) to show how to entangle photons to a 4-photon, 6-photon, 8-photon etc state with nonclassical measurement statistics.
They did not claim that they produced temporally entangled photons.
2. There is no dispute about that. But publication of a paper in a peer reviewed journal is no guarantee for the correctness of every statement of its content.
3. The very definition of entanglement contradicts the existence of temporally entangled photons. Entanglement requires a state in the Schrödinger picture belonging to the Hilbert space in question, and such a state always means a state at a fixed time.
I only evaluate as meaningless the interpretation of their results as having created temporally entangled photons.
The pattern is clear: They measured multiphoton states at different times and obtained a statistics identical with that of measuring a Bell state. In no case, they produced a temporally entangled state, since the latter is a thing that cannot be consistently defined.
4. This has nothing to do with relativistic or not. The Hilbert spaces in question are finite-dimensional, so no field theory is involved.
That's not quite what the guidelines that you quoted say. The norm in PF is that a peer-reviewed paper is presumed to be acceptable as a basis for discussion. That is not the same as accepting what the paper says as true. Generally speaking, experimental results reported by such a paper have to be accepted as true because there is no way of checking them anyway; we just have to rely on the experimentalists to accurately report what they did and what results they got. But theoretical claims can be checked and evaluated and potentially questioned here, and often are.DrChinese said:the norm in PF is that a peer-reviewed paper is considered evidence of acceptance of results
No. it is considered evidence for discussing not a personal theory, hence in the present case it establishes only that you are not discussing your own inventions.DrChinese said:However: the norm in PF is that a peer-reviewed paper is considered evidence of acceptance of results.
Please cite a definition of what it means to be temporally entangled, because this is what is criticized. Simply citing the use of the term does not make it a correctly defined term.DrChinese said:As is common in discussions I have with others with whom there are disagreements, I am the only one posting suitable references.
They use buzzwords but don't give clear explanations of what these words mean. This is a common disease in hot topics.DrChinese said:It is difficult for me to believe that, when dozens of papers say exactly the opposite of what is "self-evident".
The technique is novel and useful, but how they sell it is overhyped. Peres could have done the same in 1999 but he was more careful and not susceptible to hype.DrChinese said:The mere fact my reference was published in PRL indicates it was considered novel and that the scientific community would benefit from seeing the results.
No. This is their equation (3). It contains temporal modes, hence is a fictitious state. The physical states can be read from Fig.1. Moreover, formally the state (3) is a 4-photon state, not a Bell state.DrChinese said:3. Not true at all! They define a state of entanglement in time as:
|Ψ−>0, τab ⊗ |Ψ−>τ, 2τab = 1/2(
|Ψ+>0, 2τab |Ψ+>τ, τab
-|Ψ−>0, 2τab |Ψ−>τ, τab
-|φ+>0, 2τab |φ+>τ, τab
+|φ−>0, 2τab |φ−>τ, τab )
So that would be a precise counter-example to your claim.
Their experiment provides support for no more than what Peres already spelt out in precise language: that the statistics is as if it came from such a state. This doesn't make their technique useless, but it shows that they use careless language to sell their result as more than it is.DrChinese said:Their experiment provides support for this equation.
A. Neumaier said:1. ...The claim is only identical behavior of the statistics, not the creation of a meaningless temporally entangled state! ... Clearly it means no more than pairs of photons that reproduce the statistics of entangled photons, in the above as-if sense of Peres.
... It does, not, however, justify talking of temporally entangled 2-photon states or biphotons, since quantum-mechanical states are mathematically well-defined objects with a clear single time meaning.
2. Who of the authors of your primary source is a Nobel prize winner? Which year?
1. Still no support provided for your position. These papers are from 2012, and there is nothing refuting them in the literature since?A. Neumaier said:1. But correctness issues are independent of that and can still be discussed without accepting them.
2. Please cite a definition of what it means to be temporally entangled, because this is what is criticized. ... No. This is their equation (3). It contains temporal modes, hence is a fictitious state.
3. Moreover, formally the state (3) is a 4-photon state, not a Bell state.
4. Their experiment provides support for no more than what Peres already spelt out in precise language...
PeterDonis said:That's not quite what the guidelines that you quoted say. The norm in PF is that a peer-reviewed paper is presumed to be acceptable as a basis for discussion. That is not the same as accepting what the paper says as true. Generally speaking, experimental results reported by such a paper have to be accepted as true because there is no way of checking them anyway; we just have to rely on the experimentalists to accurately report what they did and what results they got. But theoretical claims can be checked and evaluated and potentially questioned here, and often are.
This account might be consistent, but is not insisted upon us by equation (3).This result was described by Einstein as ”spooky action at a distance”. In the scenario we present here, measuring the last photon affects the physical description of the first photon in the past, before it has even been measured. Thus, the ”spooky action” is steering the system’s past. Another point of view that one can take is that the measurement of the first photon is immediately steering the future physical description of the last photon. In this case, the action is on the future of a part of the system that has not yet been created.