A Possibilities of Time-Independent Entangled Photons

[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!

 

[DrChinese]

1. 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:

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: ...

2. This is quite the opposite of what you claim!

1. I agree with a lot of what you say here about the 2004 article.

2. Not so fast! I didn't make any claims about this paper for you to dispute.

There has been ongoing development in the area of temporal entanglement. Some of it follows this Brukner paper, which is highly cited. And some of it follows somewhat similar thinking with respect to the Leggett Garg argument (see for instance Leggett-Garg Inequalities, 2013).

Other development has been has been along the line of the entanglement swapping variants we have been discussing. My point is that the Megidish 2012 paper has very specific comments about creation of temporal Bell states of entanglement (what you call fictitious states); and I do claim they meant what they said. Oh, and yes - I believe them. But you are correct if you say that doesn't mean its true, whether I agree with them or not. And whether the peer review team agreed with them or not.

In general, it is becoming more and more clear there *is* something called temporal entanglement, as demonstrated by Megidish. The other lines of inquiry have not produced as strong an argument as that did, IMHO. Again, each is entitled to their own opinion as to what is convincing - and what is not. And yes, there are a series of references I will be adding on the topic - these must be read as an ongoing narrative. I.e. those along the lines of Brukner-2004 and Leggett-Garg.

 

[DrChinese]

But you didn't consider the full context:

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.

That's funny. Yours is the semi-classical argument! You count photon number classically (they either exist or they don't), ignoring the full quantum context which we agree is of necessity. In that view, you count down a 4 photon state from 4 to 0 - one at a time. You are entitled to have that method, sure. But you can't get at the full quantum context in that manner. The various entangled states - Bell, GHZ, W, etc - don't work that way. They are isomorphic (in statistical prediction) as to measurement (annihilation) order, so such countdown makes no sense at all. Ditto with entangled photon creation order.

This is experimentally confirmed, as we all agree. So why pick out one specific scenario as being "fictitious" (pseudo-) when they all predict the same thing and operate near identically?

 

[A. Neumaier]

I didn't make any claims about this paper for you to dispute.

You claimed:

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.

and Brukner et al. was the complete list of ''some references'' that you gave. Thus I could assume that it contained the ''general conclusion"....

Anyway, I discussed the paper independent of your claims.

There has been ongoing development in the area of temporal entanglement. Some of it follows this Brukner paper, which is highly cited. And some of it follows somewhat similar thinking with respect to the Leggett Garg argument (see for instance Leggett-Garg Inequalities, 2013).

So I'll read this paper too and examine its claims!

My point is that the Megidish 2012 paper has very specific comments about creation of temporal Bell states of entanglement

states that fall from heaven, wihout any theoretical backup. If they didn't have the result of their experiment, it would not be clear at all why their formulas should be valid. To be convincing, their formulas should be derived from quantum mechanics, not just stated and shown to agree with their results!

Suppose someone else suggests an experiment that hasn't been done yet, and that doesn't lead to the Bell statisitcs but where it is claimed that the results would violate the Brukner et al. inequality. How could you (or they) decide

1. whether their claim is valid?
2. which temporally entangled state the setup corresponds to?

Trying to come up with an answer must of course be based on standard quantum theory (where states exist only for fixed time settings). This direcly leads to the (unsolvable) problems a notion of temporally entangled states has.

In general, it is becoming more and more clear there *is* something called temporal entanglement, as demonstrated by Megidish.

Why? All that has ever been demonstrated on this subject are time correlations violating a hidden variable bound. Taking this as ''clear'' evidence for something called temporal entanglement (and even, as you claim, as evidence for temporally entangled states) is unfounded, in view of the difficulties discussed by Brukner et al..

 

[A. Neumaier]

That's funny. Yours is the semi-classical argument!

You argue with equations that come out of the blue (rather than from standard quantum mechanics), combined with informal talk that has nothing to do with the (shut up and calculate) quantum formalism, hence does not deserve the label 'quantum' but at best 'semiclassical', or perhaps I should have said 'informal'!

You count photon number classically (they either exist or they don't), ignoring the full quantum context which we agree is of necessity. In that view, you count down a 4 photon state from 4 to 0 - one at a time.

This is neither classical nor semiclassical but it is what Fig.1 clearly depicts. It follows from standard quantum theory that the system in this setup is at each time in an N-photon state, where N changes as I described. It is a well-known fact that the measurement of a single photon reduces the photon number of the measured state by one. Without this fact it would be impossible to analyze any Bell type experiment!

But you can't get at the full quantum context in that manner.

The full quantum context can only be obtained by applying standard quantum dynamics to the experimental setup, which I did, and not by handwaving arguments that don't make any connection to the dynamics, which you did.

The various entangled states - Bell, GHZ, W, etc - don't work that way. They are isomorphic

Please describe the isomorphism, or don't use this word, which has a precise mathematical meaning. Words don't decide, only precise logical arguments do!

This is experimentally confirmed, as we all agree.

Only the final statistics is experimentally confirmed. Its derivation from theory is completely missing in the papers by the experimentalists, and replaced by ''suggestive'' formulas without a definite formal meaning that appear without theoretical support.

So why pick out one specific scenario as being "fictitious" (pseudo-) when they all predict the same thing and operate near identically?

Fictitious is a nowhere clearly defined notion of temporally entangled state. The states appearing in standard quantum mechanics are without exception states at a fixed time. Introducing deviations from this without strong theoretical support is poor scientific practice, even when it is published in renowned journals.

 

[PeterDonis]

You count photon number classically (they either exist or they don't)

For the experiments under discussion, with a standard NRQM analysis, that is how photon number is counted: by photon preparations and photon detections. Those are discrete.

It is true that the preparation process using BBO crystals is probabilistic--it won't always produce an entangled pair that meets the requirements--but we are only considering runs where it does produce the required entangled pair, and that pair is a biphoton--two photons--even according to you.

So in a standard NRQM analysis, once we know the times of each preparation and each measurement, we can indeed count photons classically and assign a definite number to how many exist at any given time. And, as you have said, relativistic effects are negligible in these experiments, so a standard NRQM analysis is valid.

 

[DrChinese]

1. You argue with...

2. Only the final statistics is experimentally confirmed. Its derivation from theory is completely missing in the papers by the experimentalists, and replaced by ''suggestive'' formulas without a definite formal meaning that appear without theoretical support.

3. Introducing deviations from this without strong theoretical support is poor scientific practice, even when it is published in renowned journals....

1. I am quoting authors verbatim (something that you have yet to consider). My arguments are generally not original, but tend to follow state of the art in the entanglement world. Note that in my neck of the woods, "state of the art" tends to be 5 or 10 years old at least. It takes me at least 5 years to fully digest all the new stuff, it's like a flood.

[Snippy comment deleted-DrC] I will point out that the Megidish experiment was in first fact introduced here in a PhysicsForums QM thread shortly after it came out - actually the next day, 20 September 2012. And started by ???. Go on, make a guess...


2. Experimentally confirmed, the magic words. Yet... apparently "real" Bell states appear in all of the virtually identical entanglement swapping scenarios (referenced) except one - which is "fictitious". So apparently you agree with the theory in most cases, you simply reject it when inconvenient - or violates one of your premises. We are supposed to learn from experiment.


3. [Snippy comment deleted-DrC].

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Thread reopened.

 

[DrChinese]

I'd like to apologize* to @A. Neumaier and @PeterDonis for anything I have posted which sounds snippy, disrespectful or unnecessarily argumentative. In re-reading some of my posts in this thread, I sense I may have crossed the line a few times. I have deleted a portion of my post #111 which was intended with a touch of humor (there was a smiley face), but reads poorly otherwise.

I greatly respect both of these members, and thank them and everyone else for their time in our often "lively" discussions on quantum foundations.


*This apology is unrelated to the closing/re-opening of the thread.

 

[mattt]

1. I am quoting authors verbatim (something that you have yet to consider). My arguments are generally not original, but tend to follow state of the art in the entanglement world. Note that in my neck of the woods, "state of the art" tends to be 5 or 10 years old at least. It takes me at least 5 years to fully digest all the new stuff, it's like a flood.

[Snippy comment deleted-DrC] I will point out that the Megidish experiment was in first fact introduced here in a PhysicsForums QM thread shortly after it came out - actually the next day, 20 September 2012. And started by ???. Go on, make a guess...


2. Experimentally confirmed, the magic words. Yet... apparently "real" Bell states appear in all of the virtually identical entanglement swapping scenarios (referenced) except one - which is "fictitious". So apparently you agree with the theory in most cases, you simply reject it when inconvenient - or violates one of your premises. We are supposed to learn from experiment.


3. [Snippy comment deleted-DrC].

You have an experimental set up, some experimental results and a theoretical explanation of what's going on.

In the other cases, the theoretical explanation is OK.

In the case we are discussing, the "theoretical explanation" in that paper uses undefined concepts ("state at a fixed time of a biphoton that doesn't exist") to account for the statistics.

There is no need for that. Both Peter and Arnold showed you that there is no need for inventing new terms here.

Our old NRQM theory correctly explains this case as well, without invoking any fictional terms.

 

[A. Neumaier]

My point is that the Megidish 2012 paper has very specific comments about creation of temporal Bell states of entanglement (what you call fictitious states); and I do claim they meant what they said. Oh, and yes - I believe them.

In general, it is becoming more and more clear there *is* something called temporal entanglement, as demonstrated by Megidish.

Something on the experimental level, but something without having a well-defined concept on the theoretical side.

Note that there are different levels of theoretical standards in different aras of physics:

Mathematical physics:
All concepts are rigorously defined and all arguments satisfy all demands of logic.

Theoretical physics:
All concepts are properly defined and deductions are reasonably complete, but concepts and arguments satisfy only relaxed demands, justified by plausibility arguments where full rigor is lacking. For example, proofs may be given by example instead of in full generality, and convergence of series, interchanges of limits, domain issues and other delicate mathematical aspects may be left unaddressed as long as the results of the formal manipulations look convincing from the physical point of view.

Experimental physics:
Concepts are used to throw light on the experimental study, even if they lack theoretical support. Theoretical aspects may be left unaddressed as long as the results of the formal manipulations look convincing from the experimental point of view.

This explains why the over hundred papers that you mentioned but didn't quote verbatim use the concept of temporally entangled states although it cannot be given a clear theoretical meaning. Experimentalists and their readership are free to use these, but they should not mistake them for theoretically well-founded concepts.

I am quoting authors verbatim (something that you have yet to consider).

I was also quoting authors verbatim (something that you have yet to notice).

Yet... apparently "real" Bell states appear in all of the virtually identical entanglement swapping scenarios (referenced) except one - which is "fictitious".

real := having a dynamical meaning, since it can appear in a Schrödinger (or, for mixed statex, von Neumann) equation.

fictitious := any othe use of the word state.

Apart from that I have nothing substantial to add to our discussion, and will leave it at that. Both of us have clearly expressed our views and become only repetitive.

 

[DrChinese]

We've probably exhausted discussion of the Megidish experiment at this point. I found this nice bit which ties in nicely to our discussion on consideration of the entire context: @A. Neumaier said: "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." (Of course I agree.) Hopefully, this version of entanglement swapping is something we can all agree produces genuine Bell states.

Delayed-choice gedanken experiments and their realizations
Xiao-song Ma, Johannes Kofler, Anton Zeilinger (2016)
"The relative temporal order of measurement events is not relevant... To interpret quantum experiments, any attempt in explaining what happens in an individual observation of one system has to include the whole experimental configuration and also the complete quantum state, potentially describing joint properties with other systems. According to Bohr and Wheeler, no elementary phenomenon is a phenomenon until it is a registered phenomenon (Bohr, 1949; Wheeler,1984). In light of quantum erasure and entanglement swapping, one might like to even say that some registered phenomena do not have a meaning unless they are put in relationship with other registered phenomena (Ma et al., 2012)."

[See related diagram below from the reference.]

If you try to analyze the individual component measurements ("some registered phenomena") without considering their relative relationship to other measurements in the whole configuration, the complete quantum state might not be evident. You can see from the diagram attached that the entire quantum setup starts with N=4 photons*. But it does not qualify as temporal entanglement.

*Or perhaps N=2 biphotons, depending on perspective.

 

[A. Neumaier]

Hopefully, this version of entanglement swapping is something we can all agree produces genuine Bell states.

Which version? The paper you cited is a survey of many experiments!

Note also that the paper never mentions temporal entanglement or temporally entangled states. In a survey that has several subsections about entanglement swapping, this should make you question how established the notion of temporal entanglement is!

has to include the whole experimental configuration and also the complete quantum state, potentially describing joint properties with other systems.

The notion of 'complete quantum state' of the experiment is used here, without any hint of what might be meant by it. Since the term seems to make sense to you, could you please provide a definition of this term? Or does your confession

the complete quantum state might not be evident.

mean that you also grope in the dark?

Giving a whole experiment a 'complete quantum state' may make sense informally, but not mathematically.

According to quantum mechanics as established since 1930, any experiment (involving pure states only) with measurements at different times is completely described by a continuum of quantum states $\psi(t)$ for all times $t$ during the experiment, governed by the Schrödinger equation between measurements and appropriate projections at measurements.

This is a complete description from which all measurement statistics can be deduced. Thus any sensible notion of a 'complete quantum state' $\psi_c$ for the experiment must give a definite mathematical rule how to convert the continuum of quantum states $\psi(t)$ into the alleged complete quantum state $\psi_c$. Perhaps you could be so kind and point to such a conversion rule.

In the absence of such a conversion rule, talk about the 'complete quantum state' is merely wishful thinking, no matter how many publications are devoted to its informal use. The latter just means that the referees of papers on interesting experiments put very little constraint on the informal usage of undefined or only vaguely defined concepts.

 

[Morbert]

real := having a dynamical meaning, since it can appear in a Schrödinger (or, for mixed statex, von Neumann) equation.

fictitious := any othe use of the word state.

So, considering one of the terms on the right hand side of equation (3) in the Megidish paper, would you object to a sketch like this?

$$U(t)|\phi^-\rangle^{0,2\tau}_{1,4}|\phi^-\rangle^{\tau,\tau}_{2,3}|\epsilon_\mathrm{ready}\rangle_{1,4}^{0,2\tau}|\epsilon_\mathrm{ready}\rangle_{2,3}^\tau = |\epsilon^-\rangle_{1,4}^{t,2\tau+t}|\epsilon^-\rangle_{2,3}^{\tau+t}$$where $\epsilon$ are environmental/detector degrees of freedom to permit a unitary description of detection.

 

[PeterDonis]

would you object to a sketch like this?

Such a state would be "fictitious" by the definitions @A. Neumaier gave, since it cannot appear in a Schrodinger equation (which only allows states where all the kets refer to the same time).