Possibilities of Time-Independent Entangled Photons

[PeterDonis]

If my references make claims that violate theory

What theory? That's the question I've been trying to get an answer to. What theory is being used to justify the equations that have been referenced? It can't be standard NRQM using the Schrodinger equation. So what theory is it?

Again, this question only matters if it is being claimed that the "temporal mode" Bell States, i.e., Bell states involving pairs of photons that have never coexisted, are physically real. If the only claim is that these states are used for computation because they make correct predictions, and are not treated as being physically real, then there is no issue. But you have said in other threads that you are using a realist interpretation. If that is the case, then there is an issue. For one thing, you would need to show that the papers you reference are also using a realist interpretation, and provide the necessary theoretical framework to justify such an interpretation for the case of Bell States of photons that never coexist. Just mathematically rearranging equations doesn't do that, for reasons that @A. Neumaier has already stated better than I have.

 

[PeterDonis]

you have the significance backwards. Peres had discovered his novel point before experimental realization of entanglement swapping had confirmed it. His description is accurate of course, and I would agree with it today exactly as written. Since then however: A large body of theoretical and experimental work has followed.

Has any of that large body of theoretical and experimental work made the claim that "temporal mode" Bell States, i.e., Bell States involving pairs of photons that never coexist, are physically real? Or has it only claimed that those states can be used to make predictions because the predictions match the observed statistics?

 

[DrChinese]

1. I don't dispute any of the results of those experiments. Just the wording.

In the case where photon1 is destroyed (for all observers) before photon4 is created, having "entanglement-like statistics" is not the same as having "a biphoton1,4 entangled state at a fixed time t_0" (because the latter cannot exist in this case).

If you (or others) want to call that situation "photon1 and photon4 are 'temporally [note I corrected the spelling] entangled' " you are free to use those words, but still there isn't any biphoton1,4 state (let alone entangled biphoton1,4 state) in that case.

2. ...their wording violates the theory... But that's obviously not what they mean.

1. You are free to deny what the papers say. Again, that means you also deny there is such things as "delayed choice entanglement swapping". Because those phenomena feature the same issues you object to: namely, that a Bell state is created between photons that no longer exist - after the fact. As I point out in post #118 point 4, Peres published theory on this as early as 1999.

2. They mean what they say and I presented. And yet again, I point to the theory presented by Peres, 1999. He says: "Later, they will learn from Eve that a definite subset of her experiments ascertained the existence of a definite entangled state of their particles. ... one has to clearly understand quantum mechanics and to firmly believe in its correctness to see that there is no paradox."

So you are welcome to reject what conclusions you like, no issue from me. But if you are claiming some published authors' wording violate theory: Where is such theory published? That's a rhetorical question at this point, I don't actually want or expect an answer from you or anyone else.

 

[A. Neumaier]

1. Still no support provided for your position. These papers are from 2012, and there is nothing refuting them in the literature since?

Just refuting sloppy language never gets published. Otherwise there would be a flood of irrelevant papers, as sloppy arguments are legion.

2. I provided that definition, and then you dismissed it.

The only thing close to a definition I saw was the statement that nonclassical correlations are evidence for entanglement. But this is not a definition in the usual sense. Telling what is evidence for a crime doesn't define what a crime is....

1. Entangled state statistics are evidence of entanglement, this is well-accepted and has been for decades.

It is evidence for entanglement somewhere in the process leading to the statistics.

Peres is carefully stating precisely what it is evidence of: The setting ''behaves as if it consisted of entangled pairs of distant particles''. This is quite different from claiming that ''the two particles measured to get the statistics are entangled''!

3. Yes, it is a 4 photon state: a Product state of 2 Bell states (of entangled photon pairs). The equation is described correctly as I wrote it.

It contains temporal modes, hence is a fictitious 4-photon state, not a physical one.

The 1 and 4 photons can be demonstrated to follow perfect correlations as well as violation of Bell inequalities, something that is a certain marker of entanglement. I guess I'll have to trot out some references on that, if you are doubtful...

It means no more than that we have pairs of photons that reproduce the statistics of entangled photons, in the above as-if sense of Peres.

2. You know perfectly well that Zeilinger is co-author of three of the 5 papers I referenced, and when he won the award.

Well, but the experiments are not in question!

In question is the claim in your primary reference - whether photons can be entangled even when one partner has already been measured and no longer exists, and your claim that we have a biphoton in a Bell state (a claim that I didn't read in the papers)!

Referring to Zeilinger as authority on this matter is misleading unless you can show that he endorses this claim!

His paper that most closely resembles my primary reference is Experimental delayed-choice entanglement swapping.

The published reference is https://www.nature.com/articles/nphys2294. Let me quote a number of fragments (my labels A,B,C,...):

A: Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be ‘produced a posteriori, after the entangled particles have been measured and may no longer exist’.

B: [...] whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured.

C: Whether Alice’s and Bob’s photons can be assigned an entangled state or a separable state depends on Victor’s later choice. In Peres’s words: ‘‘If we attempt to attribute an objective meaning to the quantum state of a single system, curious paradoxes appear: quantum effects mimic not only
instantaneous action-at-a-distance but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded.

D: This means that it is possible to freely and a posteriori decide which type of mutually exclusive correlations two already earlier measured particles have.

Quote A appears in the informal introduction of the paper by Peres, but he is more careful in his formulation in the main body of his paper (care that is lost in the quote). There he says:

There can be no doubt that the particles that were independently produced and tested
by Alice and Bob were uncorrelated and therefore unentangled. Each one of these particles may well have disappeared (e.g., been absorbed) before the next particle was produced, and before Eve performed her tests. Only the records kept by the three observers remain, to be examined objectively.

Thus: No entanglement! Peres continues:

How can the appearance of entanglement arise in these circumstances? The point is
that it is meaningless to assert that two particles are entangled without specifying in
which state they are entangled

Thus: Only the appearance of entanglement! Peres continues:

If this simple rule is forgotten, or if we attempt to attribute an objective meaning to the quantum state of a single system, curious paradoxes appear: quantum effects mimic not only instantaneous action-at-a-distance but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded.

The paper you cited takes part of the latter quote (see C above) out of context, thus altering its meaning. In reality, as Peres asserts, there is no influence of future actions on past events - no matter what Alice or Bob do, the photons measured are unentangled and only appear entangled! This invalidates the claim in quote D above. (Taken literally, quote D is anyway nonsense: Already measured particles have precisely the measured correlations; there is nothing at all left to be decided!)

My conclusion is that the paper is sloppily argued, in spite of Zeilinger's name on it.

*

Quote B amounts to a redefinition (R) of entanglement by:
(R) entangled := showing quantum correlations.

In particular, the definition (R) does not at all involve wave functions or states. Neither states nor biphotons are involved but just statistical correlations! This is in contradition to Peres' statement quoted above. For Peres, the authoritative definition is the textbook definition (T), where a quantum system is defined to be entangled by:
(T) entangled := its wave function (following the Schrödinger dynamics) is not separable.

A redefinition is of course in principle acceptable once agreed upon, but it must be made explicit that it alters the tradition before 2012.

Clearly (R) and (T) imply different meanings, giving rise to the misunderstandings under discussion. Moreover, the pair correlation statistics does not determine a unique state (except for 100% efficient Bell experiments, which is never the case). Hence one cannot obtain from entangled systems in the sense of (R) information about corresponding states. The nonphysical effective states written down in the papers are idealizations not warranted by the experimental inefficiencies.

In the paper of Zeilinger et al, both photon 1 and photon 4 do not exist at the time of the entanglement swap.

... and - according to Peres, definition (T) - they are uncorrelated and only appear correlated.

According to the redefinition (R), they are entangled aposteriori, but this is known only if the full experiment is performed. If not, what would be the state of the (not coexisting) 2-photon pair???

a Bell state is created between photons that no longer exist - after the fact. As I point out in post #118 point 4, Peres published theory on this as early as 1999.

No. As I showed, Peres 1999 published theory implying that, in an entanglement swapping experiment, two uncorrelated photons appear to be entangled, and not more.
That a Bell state is created between photons 1 and 4 is not even claimed in the 2012 paper with Zeilinger as coauthor!

 

[PeterDonis]

You are free to deny what the papers say.

The issue is not whether anyone in this thread is "denying" what the papers say. It is a question of what the papers actually say. Do they actually say that there is a physically real Bell state involving pairs of photons that never coexist? Or do they only say that such a state can be used for computation because it makes correct predictions about the statistics, without claiming that it is physically real?

If they only say the latter, there is no issue at all. If they say the former, then there is an issue. But you have not yet expressed an opinion specifically on what you think they say in this respect, so we don't know yet whether there is actually an issue or not. I have said that in previous threads you used a realist interpretation of QM, which would imply that you think the papers are saying the former; but I might be wrong.

 

[DrChinese]

Has any of that large body of theoretical and experimental work made the claim that "temporal mode" Bell States, i.e., Bell States involving pairs of photons that never coexist, are physically real? Or has it only claimed that those states can be used to make predictions because the predictions match the observed statistics?

I was hoping you understood that the general theory being applied in this "temporal Bell State" experiment is exactly the same as the "delayed choice" case (where there is a much larger body). That being that a Bell State can be created for photon(s) that no longer exist. See Peres 1999 as mentioned in post #118.

Regardless of anything you have presented previously either way: Entanglement is evidenced by violation of CHSH or other inequalities violating local realism. As we have agreed, another term for this is quantum nonlocality. Any violation of such inequalities is de facto evidence of entanglement. That is standard theory. There are no experimental realizations of CHSH violations from separable Product states. I.e. there is no such thing as reproducing Entangled state statistics (Bell states) outside of the existence of entanglement. From Delayed-choice gedanken experiments and their realizations summarizing theory and experiment as of 2014:

"When two systems are in an entangled quantum state, the correlations of the joint system are well defined but not the properties of the individual systems (Einstein et al., 1935; Schrodinger, 1935). Peres raised the question of whether it is possible to produce entanglement between two systems even after they have been registered by detectors (Peres, 2000). Remarkably, quantum mechanics allows this via entanglement swapping (Zukowski et al.,1993)."

If you think the case where only photon 1 is measured before the swap is entirely different then the case where both 1 and 4 are measured before the swap, then that would be a different story. But it would surprise me.

 

[PeterDonis]

@DrChinese, nothing in your post #128 answers the question I posed in post #127. The latter question just requires a one sentence answer. It does not require rehashing the references you have given.

 

[mattt]

1. You are free to deny what the papers say. Again, that means you also deny there is such things as "delayed choice entanglement swapping". Because those phenomena feature the same issues you object to: namely, that a Bell state is created between photons that no longer exist - after the fact. As I point out in post #118 point 4, Peres published theory on this as early as 1999.

2. They mean what they say and I presented. And yet again, I point to the theory presented by Peres, 1999. He says: "Later, they will learn from Eve that a definite subset of her experiments ascertained the existence of a definite entangled state of their particles. ... one has to clearly understand quantum mechanics and to firmly believe in its correctness to see that there is no paradox."

So you are welcome to reject what conclusions you like, no issue from me. But if you are claiming some published authors' wording violate theory: Where is such theory published? That's a rhetorical question at this point, I don't actually want or expect an answer from you or anyone else.

Not their wording, but your interpretation of their wording.

I interpret their wording just like Peter and Arnold, which entails no problem with theory.

 

[PeterDonis]

They mean what they say

Words don't have unique unambigous meanings. Particularly when the domain of discussion is physics and the actual content of theories, at least as far as making predictions is concerned, is contained in math, not ordinary language.

and I presented.

If what you had already presented in this thread were sufficient for me to be confident of an answer to the question I posed to you in post #127, I wouldn't have bothered to pose the question. So continuing to refer to what you have already said is not helpful in answering that question.

 

[DrChinese]

The issue is not whether anyone in this thread is "denying" what the papers say. It is a question of what the papers actually say. Do they actually say that there is a physically real Bell state involving pairs of photons that never coexist? Or do they only say that such a state can be used for computation because it makes correct predictions about the statistics, without claiming that it is physically real?

If they only say the latter, there is no issue at all. If they say the former, then there is an issue. But you have not yet expressed an opinion specifically on what you think they say in this respect, so we don't know yet whether there is actually an issue or not. I have said that in previous threads you used a realist interpretation of QM, which would imply that you think the papers are saying the former; but I might be wrong.

Yes, they actually say "there is a physically real Bell state involving pairs of photons that never coexist" in the following quote.

Eisenberg et al say: "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. ... In conclusion, we have demonstrated quantum entanglement between two photons that do not share coexistence. Although one photon is measured even before the other is created, full quantum correlations were observed by measuring the density matrix of the two photons, conditioned on the result of the projecting measurement. This is a manifestation of the non-locality of quantum mechanics not only in space, but also in time."

DrChinese says: I agree with everything in the above quote exactly as expressed.

I thought this has been made clear over and over. And yes, I am quite aware that you are not convinced by what I have presented in the various posts. Again, I do not want to argue with anyone, nor do I wish to continue is circles. I have reasonably explained and supported everything I have said. But I think at this point there is little I can add that would change any viewpoints, or be worth more of our collective time and energy.

Note: I will look for additional references to support the equivalence/relationship of entanglement to violations of Bell inequalities (i.e. one implies the other). I had not bookmarked papers on that as I assumed it was well known. I can post that in a new Foundations thread, as it is actually a different subject. If you think it would be helpful to move our discussion in this thread around my references to a separate thread, that would be fine. I would prefer they not be deleted, however.

 

[mattt]

Yes, they actually say "there is a physically real Bell state involving pairs of photons that never coexist" in the following quote.

Eisenberg et al say: "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. ... In conclusion, we have demonstrated quantum entanglement between two photons that do not share coexistence. Although one photon is measured even before the other is created, full quantum correlations were observed by measuring the density matrix of the two photons, conditioned on the result of the projecting measurement. This is a manifestation of the non-locality of quantum mechanics not only in space, but also in time."

DrChinese says: I agree with everything in the above quote exactly as expressed.

I thought this has been made clear over and over. And yes, I am quite aware that you are not convinced by what I have presented in the various posts. Again, I do not want to argue with anyone, nor do I wish to continue is circles. I have reasonably explained and supported everything I have said. But I think at this point there is little I can add that would change any viewpoints, or be worth more of our collective time and energy.

Note: I will look for additional references to support the equivalence/relationship of entanglement to violations of Bell inequalities (i.e. one implies the other). I had not bookmarked papers on that as I assumed it was well known. I can post that in a new Foundations thread, as it is actually a different subject. If you think it would be helpful to move our discussion in this thread around my references to a separate thread, that would be fine. I would prefer they not be deleted, however.

Yes, sloppy wording again. I interpret it as saying that they obtain the same statistics, and calling it "the same state". (Maybe it is customary to call it that way in some circles).

But surely you understand that there isn't a fixed time t_0 where a biphoton1,4 state exist, right?

 

[A. Neumaier]

Yes, they actually say "there is a physically real Bell state involving pairs of photons that never coexist" in the following quote.

Eisenberg et al say: "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. [...]"

This is Megidish et al., not Eisenberg et al..They claim this but they do not prove it. There is no general way to determine from a pair statistics a state.

What they prove is that the fictitious 4-particle state (3) involving temporal modes projects to a fictitious Bell state for the photon pair 1+4 when in this state a Bell measurement on the photon pair 2+3 is made.

But in their experiment they first make a measurement on photon 1, which according to standard quantum mechanics projects the (fictitious, but assumed physical) 4-photon state to a 3-photon state no longer involving photon 1. Then they make a Bell measurement on the photon pair 2+3, which according to standard quantum mechanics projects the 3-photon state to a 1-photon state only involving photon 4.

Thus their theoretical argument about projecting the state (3) to a Bell state for the photon pair 1-4 is irrelevant for their actual experimental setting.

The correct theoretical prediction for the statistics for the experiment can therefore not be due to their argument. Instead it is a consequence of the composition of the POVMs (or rather quantum operations, since classical measurement results are produced during the projections) determined by the physical evolution depicted in their Fig.1, where no 4-photon state and no fictitious temporally entangled states appear.

DrChinese says: I agree with everything in the above quote exactly as expressed.

Then you should be able to explain what is wrong in my analysis.

 

[PeterDonis]

surely you understand that there isn't a fixed time t_0 where a biphoton1,4 state exist, right?

@DrChinese agreed with this in a post a while back in this thread.

 

[PeterDonis]

I thought this has been made clear over and over.

It has also been stated over and over that the wording you keep quoting is ambiguous. You have now confirmed that you are interpreting it as asserting the existence of a physically real Bell state involving two photons that never coexist. But two others in this thread (@A. Neumaier and @mattt) are interpreting it to mean the other claim I described, that it only asserts that the statistics are correct. My personal inclination is also towards the latter interpretation, since it does not require me to believe that multiple authors would be making an assertion that (a) requires a realist interpretation of QM, and moreover, one that goes considerably beyond what other realist interpretations assert, and (b) is an obvious contradiction to the math of NRQM (and you have agreed to this since you have agreed that there is no time at which a Bell state involving the never coexisting photons exists in NRQM), so either it has no mathematical justification whatsoever, or it is relying on some other mathematical model of the underlying dynamics that I can't find anywhere and that has not been referenced anywhere in this thread or in any of the papers referenced in this thread.

Given all this, your blithe assumption that you have given all the information that needs to be given, many times over, and that we are simply being obstinate in refusing to accept established physics, does not seem justified to me. But it also does not seem to me that we're going to resolve that here since it hinges on different, incompatible intepretations of wording in the papers referenced, and what we disagree on has nothing to do with the experimental results, which we all agree on.

 

[PeterDonis]

I will look for additional references to support the equivalence/relationship of entanglement to violations of Bell inequalities (i.e. one implies the other).

That's not what you need to look for, if you are going to look for something. What you need to look for is references that justify the use of the term "entanglement" as asserting a physically real Bell state involving photons that never coexist, when there is never any such wave function at any time in the standard NRQM treatment of these experiments.

Equivalence of entanglement to Bell inequality violations, by itself, is irrelevant to that point, since it could just be taken to be true by definition. Even defining "entanglement" as using a Bell state wave function to make predictions, by itself, is irrelevant, since that can be done using a non-realist interpretation of QM that does not make any claim that the Bell state wave function is physically real. You are claiming that the Bell state wave function is physically real, even though no such thing ever appears in the standard NRQM treatment, so what you need to look for is references justifying that claim.

 

[DrChinese]

1. But in their experiment they first make a measurement on photon 1, which according to standard quantum mechanics projects the 4-photon state to a 3-photon state no longer involving photon 1.

2. Then they make a Bell measurement on the photon pair 2+3, which according to standard quantum mechanics projects the 3-photon state to a 1-photon state only involving photon 4. Thus their theoretical argument about projecting the state (3) to a Bell state for the photon pair 1-4 is irrelevant for their actual experimental setting.

The correct theoretical prediction for the statistics for the experiment can therefore not be due to their argument. Instead it is a consequence of the composition of the POVMs determined by the physical evolution depicted in their Fig.1, where no 4-photon state and no fictitions temporally entangled states appear.

Then you should be able to explain what is wrong in my analysis.

Finally, some serious meat to discuss.

1. OK, Let's try your path as a hypothesis. After measurement of P1 as (say) V>, I would then conclude that P2 is H> (per the 1 & 2 initial entangled state). At this point, P2 has no connection whatsoever to any other system in the universe. P3&4 are entangled. So that makes the 3 photon state a Product state of P2 ⊗ (P3&4).

2. We do the Bell State Measurement (BSM) on P2 & P3. And let's suppose we get an H>V> outcome I'm not really sure how we make P3 distinguishable from P2 though, as in this view P2 is identified as H> already. Which means P3 is V> and therefore P4 is H>. OK, that works out fine.

3. But here is where the problem arises. You can't violate a CHSH inequality with this sequence - and you can't have perfect correlations either. Obviously, we need to have perfect correlations (or anticorrelations) between P1 and P4 - that's pretty basic, right? How are those going to happen? There are essentially an large (infinite?) number of angle settings at which such correlations should appear. We can make the example work out in the following manners:

a) We consider only this one case, which of course is a very special case. No, let's agree we can't do that.
b) We consider the P2/P3/P4 a textbook case of quantum teleportation from P2 to P4. That is a reasonable description, no doubt, and I am pretty sure everything can work out fine in that view. Let's agree to this.

Except for one problem. Quantum teleportation is a one-way protocol. The P4 final state must occur after the BSM on P2 and P3. But we already know that it is possible to alter the timing of the measurement of P4 so it occurs BEFORE the BSM. That changes this setup into the Delayed Choice Entanglement Swapping case. If that happens, there is no teleportation from P2 to P4 possible. And yet, the large number of perfect correlations between P1 and P4 remain - just as in our b) option above. In fact, there is nothing to connect these photons at this point at all to each other other than random chance.

Now, to encode the possible perfect correlations between P1 and P4 in this Delayed Choice version, we would need a very large (possibly infinite) amount of information to be embedded in their partners P2 and P3. OK, that's reasonable. But that won't fly either. That's because the BSM cannot distinguish more than 4 cases (one of the 4 Bell states). And there are actually only 2 different relevant outcomes from those 4 states: either P1 and P4 are correlated, or P1 and P4 are anti-correlated. One bit of information is all that can be extracted from the BSM. So how can P1 and P4 be perfectly correlated based on a single bit of information.

In other words: As you vary the detection time of P4, to follow your reasoning, there must be a change in the statistics when P4's detection occurs prior to the BSM. That's because at some point there is no teleporation possible since teleportation is one way only. But we know those statistics don't change. We learned that from the Megidish et al experiment and one the papers it references, the Ma et al experiment. In both cases, the statistics are the same - just as I have written in post #117. So the b) option must be ruled out too. QED.

 

[PeterDonis]

You can't violate a CHSH inequality with this sequence

Sure you can. I explicitly showed you the math in a prior thread. You can use the standard NRQM framework, with the Schrodinger equation applied to a wave function that evolves in time, to account for inequality violations for any ordering of the measurements, including the case where photons 1 & 4 never coexist. What you can't do with the standard NRQM framework is to say that there is a Bell state involving photons 1 & 4, because there never is one. In the standard NRQM framework, in the case where photons 1 & 4 never coexist, the inequality violations are enforced by including the detector that measures the first of the two photons (photon 1 in your formulation) in the wave function, with the result that was recorded. That's what I did in the explicit math I showed you in that previous thread.

As far as I can tell, what @A. Neumaier is describing is the same thing I showed you in that math, just using ordinary language (and assuming an underlying formulation using POVMs, which is mathematically equivalent to the formulation using pure states, wave functions, and unitary operators that I used).

 

[DrChinese]

1. Sure you can. I explicitly showed you the math in a prior thread. You can use the standard NRQM framework, with the Schrodinger equation applied to a wave function that evolves in time, to account for inequality violations for any ordering of the measurements, including the case where photons 1 & 4 never coexist.

2. What you can't do with the standard NRQM framework is to say that there is a Bell state involving photons 1 & 4, because there never is one. In the standard NRQM framework, in the case where photons 1 & 4 never coexist, the inequality violations are enforced by including the detector that measures the first of the two photons (photon 1 in your formulation) in the wave function, with the result that was recorded.

3. That's what I did in the explicit math I showed you in that previous thread.

1. Of course, there is experimental support for this, so we already knew it happens. And I have posted numerous accompanying theoretical treatments, all of which you dismiss but agree that the Bell state statistics will pop out at the end. Glad you acknowledge that all time ordering variations are feasible with your approach as well. Since all of them have been experimentally demonstrated.

So we agree: Measurement ordering does not matter to the quantum expectation value, any more than measurement distance does not matter to the quantum expectation value.


2. I can't believe this discussion is over whether you call the relationship between P1 and P4 a Bell state or not. You obviously *define* them as NOT in a Bell state, while every author I quote verbatim says they are. OK fine. But if this isn't a semantic issue, then...??? As I have said many times, there is no single point in time when P1 and P4 (that never co-exist) are entangled. You can't use that kind of description when they don't overlap in time. We agree on that.


3. If you know where your derivation is, then go ahead and link it. But don't look for it if you don't know where it is. You don't question that the Bell state statistics are present based on your math, but you don't want to call it a Bell state.

Let's agree on this: For cases where P1 and P4 co-exist, we could call it a Bell state. Then call it a pseudo-Bell state when P1 and P4 never co-exist. (Since the statistics are the same regardless.)

 

[PeterDonis]

I have posted numerous accompanying theoretical treatments

No, you have posted references to papers that assume that you can blithely write down an entangled Bell state for photons that never coexist. None of those papers actually justify that assumption by showing what underlying dynamics replaces the standard NRQM dynamics (which does not allow any such thing) in order to make such a thing possible.

So we agree: Measurement ordering does not matter to the quantum expectation value, any more than measurement distance does not matter to the quantum expectation value.

Of course. Nobody has ever disagreed with the experimental results. That is why this discussion is in the interpretations subforum--because it's about interpretation, not experimental results.

I can't believe this discussion is over whether you call the relationship between P1 and P4 a Bell state or not. You obviously *define* them as NOT in a Bell state

I have done no such thing. I have given no definitions whatever. I have asked, repeatedly, for a justification of the use of the term "Bell state" for photons that never coexist, if that usage is taken to mean--as you mean it, and as you claim the papers you reference mean it--that that Bell state is physically real. I have yet to see any such justification. All I have seen is pointers to equations that contain Bell states with no supporting argument, and claims that if it's in the published literature, it must mean exactly what you claim it means, no matter how outlandish the claim is and no matter that no supporting argument is given. I can't believe that none of this apparently makes any difference to you at all.

As I have said many times, there is no single point in time when P1 and P4 (that never co-exist) are entangled. You can't use that kind of description when they don't overlap in time. We agree on that.

I don't see how, since despite these statements, with which I agree (and I have already said that explicitly in this discussion), you continue to claim that there is a physically real Bell state that includes photons that never coexist. To me, that claim is inconsistent with what is quoted above. But apparently not to you. And yet you wonder why this discussion has gone on so long. Of course it has, since we apparently can't even agree on what statements are consistent or inconsistent.

If you know where your derivation is, then go ahead and link it.

Derivation of what? I haven't made any claims at all. You have.

Let's agree on this: For cases where P1 and P4 co-exist, we could call it a Bell state. Then call it a pseudo-Bell state when P1 and P4 never co-exist.

Even if we were to agree on this, it would mean nothing, because our substantive disagreement is not about what we call the states, but their physical reality. You claim that a "pseudo-Bell state" is physically real. I and two others (@A. Neumaier and @mattt) disagree. We're not going to resolve that by relabeling things.

 

[PeterDonis]

That is why this discussion is in the interpretations subforum

And, as a reminder, the kind of disagreement we are having, which is not resolvable by experiment (which means it might well not be resolvable at all), is the sort of disagreement that is to be expected in this subforum.

 

[DrChinese]

@PeterDonis: our substantive disagreement is not about what we call the states, but their physical reality. You claim that a "pseudo-Bell state" is physically real. I and two others (@A. Neumaier and @mattt) disagree.

Well sure, *I* think the pseudo-Bell state is physically "real" - but I don't mind the distinguishing label so we can discuss it in more depth without everyone dismissing it out of hand. There are plenty of angles to consider.

1. To me, it's as real as *any* entangled state created in a swapping realization. We agree: The general format of the entanglement swapping experiment yields identical predictions regardless of measurement order. So I guess I would ask everyone: Does the garden variety Entanglement Swap (not temporal, no delayed choice) lead to a Bell state that you would label "real"? Some people reject that label and think it is merely statistical knowledge gained after the fact, but does not represent a physical state of entanglement between distant photons that have never interacted. Consider High-fidelity entanglement swapping with fully independent sources (2008): "Here, we fill this experimental gap and demonstrate high-fidelity entanglement swapping between entangled photon pairs emitted from time-synchronized independent sources. The resulting correlations between particles that do not share any common past are strong enough to violate a Clauser-Horne-Shimony-Holt(CHSH) inequality."

2. I personally don't see what is so different about the case where P1/P4 never co-exist. To me, one of the key elements is that the P1 measurement is done before the BSM. That is also the case in the Delayed Choice version: Experimental delayed-choice entanglement swapping (2012)

---

So I guess I'm asking in 1 and 2: Are the Bell states physically real in these experiments in which P1 and P4 co-exist? I guess this is somewhat interpretation dependent, although I am not trying to drift into that arena. Perhaps you, Arnold or someone else would care to weigh in on this.

 

[A. Neumaier]

Measurement ordering does not matter to the quantum expectation value, any more than measurement distance does not matter to the quantum expectation value.

Only in this particular setting. In general, temporal order matters for the measurement statistics - namely whenever the transition operators of the operations performed do not commute.

Does the garden variety Entanglement Swap (not temporal, no delayed choice) lead to a Bell state that you would label "real"?

Precisely when the measurement of the two photons to which the label should be attached happens after the entanglement swap. For in this case the standard quantum dynamics produces a Bell state. Thus the buzzword 'state' has a well-defined dynamical meaning.

In all other cases, the word 'state' makes no formal sense, and the only correct language is the as-if formulation used by Peres. Being a theorist, he saw the problem clearly and formulated it clearly. On the other hand, the experimentalists (Zeilinger, etc.) used ill-defined language that only described qualitatively what happens, in a roundabout way. This was sufficient (and perhaps even necessary) to sell their results as highly interesting.

 

[PeterDonis]

I personally don't see what is so different about the case where P1/P4 never co-exist.

For people who don't insist on a realist interpretation, there isn't. The statistics are the same.

The only reason we're having an issue with this at all is that you are using a realist interpretation, but you keep ignoring the fact that the math of NRQM and the Schrodinger equation, which is what your realist interpretation is supposed to be interpreting, does treat this case differently from the case where the photons do coexist, since in the latter case there is a Bell state wave function including both photons, and in the former case there isn't. Neither you nor any of your references have explained how your realist interpretation deals with this inconvenient fact.

 

[A. Neumaier]

For cases where P1 and P4 co-exist, we could call it a Bell state. Then call it a pseudo-Bell state when P1 and P4 never co-exist. (Since the statistics are the same regardless.)

I called it an unphysical, fictitious state since the statistics, had the photon pair been prepared in that state before their meaasurement, would be the same. This holds for all states defined in terms of temporal modes. All these states are useful for summarizing the behavior, but nevertheless fictitious.

 

[A. Neumaier]

How are those going to happen?

Peres described it without having to refer to fictitious states.

Note that you make a mistake when you split the analysis into what happened up to the first measurement and what happened after. As a result you lose in your argument the correlations present in the experimental setup.

It is known from the early days of quantum mechanics that to get correct results on statistics one needs to analyse the whole experiment as a single entity. When measurements are done at different times one has a quantum stochastic process. To get correct results one must therefore work with an ancilla that keeps track of all measurement results relevant for the final statistics. In this way the standard evolution of physical states according to Fig.1 of your primary reference produces the correct statistics without any paradox or contradiction.

 

[DrChinese]

I am adding some references that I hope will demonstrate the development of the ideas of Temporal Entanglement over the past 20 years. A number of papers have explored NRQM and QFT considering various elements of this. The general conclusion is that the time dimension should be placed on an equal footing with spatial dimension in QM. The approaches to this are quite varied, and there is not complete consensus on every single point. So the literature is much smaller than that of the usual spatial entanglement. I will place these in a few different posts as I present them.

---

Ref. [1] Quantum Entanglement in Time (Brukner et al, 2004):
"Conceptually, as well as mathematically, space and time are differently described in quantum mechanics. While time enters as an external parameter in the dynamical evolution of a system, spatial coordinates are regarded as quantum-mechanical observables. Moreover, spatially separated quantum systems are associated with the tensor product structure of the Hilbert state-space of the composite system. This allows a composite quantum system to be in a state that is not separable regardless of the spatial separation of its components. We speak about entanglement in space. On the other hand, time in quantum mechanics is normally regarded as lacking such a structure." ...

"Because of different roles time and space play in quantum theory one could be tempted to assume that the notion of “entanglement in time” cannot be introduced in quantum physics. In this letter we will investigate this question and we will find that this is not the case. We will explicitly derive temporal Bell’s inequalities (the notion of temporal Bell’s inequalities was first introduced by Leggett and Garg [3] in a different context; see discussion below) in analogy to the spatial ones. They are constraints on certain combinations of temporal correlations for measurements of a single quantum system, which are performed at different times. We explicitly show that quantum mechanics violates these inequalities. While mathematically two-fold correlations in space and in time are equivalent, the general spatial and temporal m-fold correlations can have completely different features." ...

"It is clear from our work, however, that it is very difficult to extend the tensor product structure beyond the two neighbouring instances in time without altering the basic principles of quantum mechanics. In fact, one of the features of entanglement in time is exactly a consequence of this difficulty: two maximally entangled events can still be maximally entangled to two other events in time (a principle we may call “polygamy” of entanglement in time). This is in contrast to the spatial entanglement which can only be “monogamous” [19].The difference between the spatial and temporal structure may ultimately be fundamental, or it may be an indication that we need a deeper theory in which the two need to be treated on a more equal footing (quantum field theory does not suffice in this sense)."

The paper discusses the concept of temporal entanglement without touching on entanglement swapping at all. It has a different approach, and there is an exact analog to CHSH as well as the Ciril'son bound. Both of these are essentially the same as with spatial entanglement. They acknowledge some of the basic issues that have already been touched on in this thread. Specifically, that QM treat time and space as different in certain respects. The Schrödinger equation is an example of that.

Interestingly: Some of you probably noticed in other thread posts that I have used the idea of Monogamy of Entanglement (MoE) as a tool to demonstrate how entanglement swapping cannot involve pre-existing correlation of the initially entangled photon pairs (P1 & P2) and (P3 & P4) with each other. In other words, there are no instances in these cases where a subset of such 4 photon systems initially have any entanglement between P1 and P4. That would violate MoE, as that would mean P1 is maximally entangled with both P2 and P4. (This is generally accepted conclusion.)

However: There is a problem with MoE when it comes to temporal entanglement. Assuming temporal entanglement is as is claimed in the paper of Megidish et al: We would need P1 to be maximally entangled with P2 at the time P1 is measured, because at that time P4 doesn't even exist. However, we also need P1 to be maximally entangled with P4 at the time P4 is measured, if a successful BSM occurred at some time. Wouldn't that violate MoE? Wouldn't violation of MoE then be proof that the Megidish paper's assumption of temporal entanglement must be false?

In Ref [1], Brukner et al discuss this point, see quote above. They claim (keep in mind this paper was 8 years before the Megidish experiment) that temporal entanglement is polygamous, even though spatial entanglement is monogamous. Funny how that works out, if correct.

 

[PeterDonis]

The general conclusion is that the time dimension should be placed on an equal footing with spatial dimension in QM.

There is no "time dimension" in NRQM. In NRQM time is not a dimension, it's a parameter.

To make time a "dimension" on the same footing with space, you need to use QFT and SR. Do any of your papers do that?

 

[DrChinese]

1. It is known from the early days of quantum mechanics that to get correct results on statistics one needs to analyse the whole experiment as a single entity.

2. When measurements are done at different times one has a quantum stochastic process. To get correct results one must therefore work with an ancilla that keeps track of all measurement results relevant for the final statistics. In this way the standard evolution of physical states according to Fig.1 of your primary reference produces the correct statistics without any paradox or contradiction.

1. I agree completely. The full context must always be understood and considered.

2. Not sure the word "stochastic" entire fits here. If the entire context is considered, there shouldn't be a stochastic process involved, right?

 

[PeterDonis]

If the entire context is considered, there shouldn't be a stochastic process involved, right?

I think that is interpretation dependent. In the MWI there would be no stochastic process since everything is deterministic. In an interpretation in which measurements have single outcomes, there would be a stochastic process.

 

[DrChinese]

1. There is no "time dimension" in NRQM. In NRQM time is not a dimension, it's a parameter.

2. To make time a "dimension" on the same footing with space, you need to use QFT and SR. Do any of your papers do that?

1. True, time is a parameter as you say. If you read the entire post, that is made clear. The objective would be to place space and time dimensions on a more equal footing. Presumably, there exist more phenomena to be discovered in temporal entanglement. Therefore a more comprehensive theory might lead us on that.

2. There are problems with accomplishing that on a number of levels, as pointed out by Brukner et al. They specifically point out some parallels and some differences between time versus space. This is an early work as I pointed out, and these difficulties are being studied still today without a satisfactory resolution. It is not even certain that there is any resolution to be had, in fact.

---

That doesn't change what is in the Megidish paper in any way of course. They already took care of the business they needed there with existing theory (of course as I, the paper authors, the peer reviewers and the 151 citing papers see it).

 

[Morbert]

2. Not sure the word "stochastic" entire fits here. If the entire context is considered, there shouldn't be a stochastic process involved, right?

To model this experiment with the decoherent histories formalism, we would use the decoherence functional $$D(\alpha,\beta) = \mathcal{N}\mathrm{tr} \left[C^{''}_\alpha U^{-1}(\tau)|\psi^-_{34}\rangle\langle\psi^-_{34}|U(\tau)C^{'}_\alpha|\psi^-_{12}\rangle\langle\psi^-_{12}|C^{'\dagger}_\beta U^{-1}(\tau)|\psi^-_{34}\rangle\langle\psi^-_{34}|U(\tau)C^{''\dagger}_\beta\right]$$where ##'## and ##''## denote components of the history before and after ##\tau## respectively. Consistent sets of histories can then represent stochastic possible sequences of events.

 

[A. Neumaier]

2. Not sure the word "stochastic" entire fits here. If the entire context is considered, there shouldn't be a stochastic process involved, right?

Repetition of the experiment produces (within the statistical errors expected) the same pair statistics but different individual measurement results. This is the hallmark of a stochastic process.

To model this experiment with the decoherent histories formalism, we would use the decoherence functional $$D(\alpha,\beta) = \mathcal{N}\mathrm{tr} \left[C^{''}_\alpha U^{-1}(\tau)|\psi^-_{34}\rangle\langle\psi^-_{34}|U(\tau)C^{'}_\alpha|\psi^-_{12}\rangle\langle\psi^-_{12}|C^{'\dagger}_\beta U^{-1}(\tau)|\psi^-_{34}\rangle\langle\psi^-_{34}|U(\tau)C^{''\dagger}_\beta\right]$$where ##'## and ##''## denote components of the history before and after ##\tau## respectively. Consistent sets of histories can then represent stochastic possible sequences of events.

... and it would produce the correct statistics from the temporal dynamics read off from the description of Fig.1 in the primary reference, without having to use any fictitious states. For whatever is done in the experiment must follow the standard quantum dynamics.

 

[A. Neumaier]

I am adding some references that I hope will demonstrate the development of the ideas of Temporal Entanglement over the past 20 years. A number of papers have explored NRQM and QFT considering various elements of this.

But you referenced only one paper, that by Brukner et al.. I'll comment on it after reading....

 

[A. Neumaier]

1. I agree completely. The full context must always be understood and considered.

But you didn't consider the full context:

1. OK, Let's try your path as a hypothesis. After measurement of P1 as (say) V>, I would then conclude that P2 is H> (per the 1 & 2 initial entangled state). At this point, P2 has no connection whatsoever to any other system in the universe. P3&4 are entangled. So that makes the 3 photon state a Product state of P2 ⊗ (P3&4).

2. We do the Bell State Measurement (BSM) on P2 & P3. And let's suppose we get an H>V> outcome I'm not really sure how we make P3 distinguishable from P2 though, as in this view P2 is identified as H> already. Which means P3 is V> and therefore P4 is H>. OK, that works out fine.

3. But here is where the problem arises. You can't violate a CHSH inequality with this sequence - and you can't have perfect correlations either.

Point 3 only follows because you dropped the photon 1 measurements from the context. The results of these measurements are still correlated with whatever happens to photon 2, because the full context must always be understood and considered.

A quantum stochastic process or a decoherence functional traces this dependence correctly, while your semiclassical argument doesn't.

 

[A. Neumaier]

Ref. [1] Quantum Entanglement in Time (Brukner et al, 2004):
"Conceptually, as well as mathematically, space and time are differently described in quantum mechanics. While time enters as an external parameter in the dynamical evolution of a system, spatial coordinates are regarded as quantum-mechanical observables. Moreover, spatially separated quantum systems are associated with the tensor product structure of the Hilbert state-space of the composite system. This allows a composite quantum system to be in a state that is not separable regardless of the spatial separation of its components. We speak about entanglement in space. On the other hand, time in quantum mechanics is normally regarded as lacking such a structure." ...

"Because of different roles time and space play in quantum theory one could be tempted to assume that the notion of “entanglement in time” cannot be introduced in quantum physics. In this letter we will investigate this question and we will find that this is not the case.

Unfortunately, while Brukner et al. introduce the words “entanglement in time” and use them several times, they give nowhere a definition of what these words should mean. Thus they do not introduce a notion of entanglement in time.

Instead they define time correlations and prove an inequality holding for the expectation values resulting from certain temporal sequences of measurements assuming local hidden variables. Reading the paper obviously should suggest that violation of their inequality constitutes “entanglement in time”, but even this is not explicitly stated but has to be inferred from reading between the lines.

Moreover, a proper notion of temporal entanglement should have a gradual interpretation, while the violation of their inequality is black and white - a slight degradation of a barely violating experimental setup that constitues temporal entanglement in their sence no longer violates their inequality, hence would have to be considered to be not temporally entangled.

This shows that a formally defined concept must be available that makes the notion independent of whether an experimental consequence satisfies some inequality. But the authors do not even hint at such a concept. Instead, they write towards the end:

One related issue we have not explored in this paper is that of mathematically describing time by associating a tensor product structure to a sequence of time instances. This seems to be necessitated by our notion of entanglement in time.

They neither explained what this notion is nor why it should necessitate the association of a tensor product structure. Instead they admit to haven't explored the problem of finding a mathematically well-defined notion! They go on to concede that such a notion would very likely require altering the basic principles of quantum mechanics:

It is clear from our work, however, that it is very difficult to extend the tensor product structure beyond the two neighbouring instances in time without altering the basic principles of quantum mechanics. In fact, one of the features of entanglement in time is exactly a consequence of this difficulty

Thus they only present many words and a vague notion without formal support.

In particular, they are very skeptical about the possibility of associating a well-defined state to a sequence of time instances. This is quite the opposite of what you claim!