Possibilities of Time-Independent Entangled Photons

[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).

 

[DrChinese]

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

2. Note also that the paper never mentions temporal entanglement or temporally entangled states.

3. In a survey that has several subsections about entanglement swapping, this should make you question how established the notion of temporal entanglement is!

1. It is in the quoted portion in italics: Ma et al 2012 (which I previously referenced).

2. I said: "But it does not qualify as temporal entanglement."

3. Well, to be fair: The title of the summary is "Delayed-choice gedanken experiments and their realizations". The Megidish experiment does not feature Delayed Choice. I didn't expect to see it referenced.

 

[A. Neumaier]

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.

No. The $\tau$-labelled states are temporal modes, hence have no interpretation as dynamical states.

 

[A. Neumaier]

1. It is in the quoted portion in italics: Ma et al 2012 (which I previously referenced).

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

I disagree. There cannot be a genuine Bell state involving photons 1 and 4 since according to Fig. 33 of the paper you quoted from, Victor's choice was made only when photons 1 and 4 already ceased to exist. But nonexistent entities cannot have dynamical states.

2. I said: "But it does not qualify as temporal entanglement."

OK, Then you changed the subject of the thread, which is temporal entanglement. Sorry for haven't missed this change of subject.

3. Well, to be fair: The title of the summary is "Delayed-choice gedanken experiments and their realizations". The Megidish experiment does not feature Delayed Choice.

The Bell projection is done after Photon 1 was measured. If instead Photons 2 and 3 had measured directly, the statistics would have been different (trivial). Thus there was a delayed choice, though, to make a difference to their citations [21,22] directly after their Fig.1 and hence something novel-sounding, only one of the choices was discussed and actualized, and the other suppressed.

 

[WernerQH]

There cannot be a genuine Bell state involving photons 1 and 4 since according to Fig. 33 of the paper you quoted from, Victor's choice was made only when photons 1 and 4 already ceased to exist. But nonexistent entities cannot have dynamical states.

I think it is a fundamental mistake to think (let alone speak) of photons as "entities". The electromagnetic field of course has dynamical states that show temporal correlations.

 

[A. Neumaier]

The electromagnetic field of course has dynamical states that show temporal correlations.

Of course. On the other hand, ''states'' involving temporal modes are clearly not states of the electromagnetic field.

I think it is a fundamental mistake to think (let alone speak) of photons as "entities".

In typical quantum optical arrangements, the state of the electromagnetic field contains between nonunitary interactions (creations and measurements) a definite number of photons (changing as 0, 2, 1, 3, 1, 0 in the arrangement depicted in Fig. 1. of Megidish et al.).

These photons can be unambiguously labeled by a label for the path they formally travel. This is the traditional terminology, universally used in quantum optics.

 

[WernerQH]

Of course. On the other hand, ''states'' involving temporal modes are clearly not states of the electromagnetic field.

I was talking about temporal correlations. I have no idea what special connotations "temporal modes" have for you.

These photons can be unambiguously labeled by a label for the path they formally travel. This is the traditional terminology, universally used in quantum optics.

The terminology is utterly familiar -- as familiar as the notorious "aether" was in Michelson's time. It was obvious to everyone that such an "entity" must exist. To me your discussion with @DrChinese sounds as pointless as the debate about how many angels can dance on a needle tip. You seem to have very restrictive ideas about the conditions under which these "entities" (photons) may be called entangled.

 

[DrChinese]

1. I disagree. There cannot be a genuine Bell state involving photons 1 and 4 since according to Fig. 33 of the paper you quoted from, Victor's choice was made only when photons 1 and 4 already ceased to exist. But nonexistent entities cannot have dynamical states.

2. OK, Then you changed the subject of the thread, which is temporal entanglement. Sorry for haven't missed this change of subject.

3. The Bell projection is done after Photon 1 was measured. If instead Photons 2 and 3 had measured directly, the statistics would have been different (trivial). Thus there was a delayed choice, though, to make a difference to their citations [21,22] directly after their Fig.1 and hence something novel-sounding, only one of the choices was discussed and actualized, and the other suppressed.

1. This is actually the point I was getting at from 2. Specifically, that for you, there is no difference between the case where 1 and 4 never co-exist , and the case where 1 and 4 never exist when the Bell State Measurement (BSM) is performed.


2. As I say, this was intended to tease out your viewpoint on the Delayed Choice Entanglement Swap. I want to make sure I have your perspective correct, so please help me along here: In your view (paraphrasing): "Photons 1 & 4 are never 'dynamically' entangled into a true Bell state. That's because photons cannot be entangled after they cease to exist." Your viewpoint would then demonstrate a consistent application of that idea between the Megidish 2012 paper (Never Co-exist) and the Ma 2012 paper (Delayed Choice).

Assuming that I have fairly represented your viewpoint: Your position is now quite distant from generally accepted physics. Basically, yours is a denial of the conclusions of all Delayed Choice Experiments - Entanglement Swapping, MZI variants, or whatever. They all create some kind of quantum state due to some future (or alternative) action being performed. Again, there are interpretations of QM that explain these phenomena in various manners, and if you are using your preferred interpretation (I assume the Thermal Interpretation) then that is an "out". But it is still not generally accepted.

3. I don't follow your comments here. Can you clarify? What do you mean by:

a. "If instead Photons 2 and 3 had measured directly"? Especially curious about "directly".
b. "only one of the choices was discussed and actualized, and the other suppressed"? Especially curious about "suppressed". All of the delayed choice experiments I cite show both the statistics for the swapping choice (creating a Bell state for 2 & 3) and the non-swapping choice (creating a Product state for 2 & 3).
c. Not entirely sure which experiment/references you mean "[21, 22]". I checked both papers and could not fit them to what you said.

 

[PeterDonis]

The terminology is utterly familiar -- as familiar as the notorious "aether" was in Michelson's time.

This is an unjustified comparison. The aether, by definition, was unobservable. The things @A. Neumaier was describing are not.

You seem to have very restrictive ideas about the conditions under which these "entities" (photons) may be called entangled.

No, he is just applying non-relativistic QM in a domain in which everyone, including @DrChinese, agrees that it works. And he is being precise about exactly what it says, and more to the point, what it doesn't say. In particular, it doesn't say that mathematical Bell states involving kets at different times occur anywhere within the dynamics; the dynamics of NRQM only include states with kets that all refer to the same time. So any talk about any states involving kets at different times, as in the papers under discussion, cannot be justified by NRQM. If there is a theoretical justification for such talk at all, it does not appear anywhere in any reference that has so far been given.

This is not a question of what words to use. If someone wants to call Bell states with kets at different times "entangled", that's a matter of words, not physics. But if someone wants to claim that such states are "real"--and @DrChinese has explicitly said in this thread that he is making that claim, and that he thinks the authors of the papers he has referenced are making that claim too--then they should be able to justify that claim with something more than just the assertion that, since the Bell states make the correct predictions, they must be real. But that claim, right now, is all we have.

 

[A. Neumaier]

1. This is actually the point I was getting at from 2. Specifically, that for you, there is no difference between the case where 1 and 4 never co-exist , and the case where 1 and 4 never exist when the Bell State Measurement (BSM) is performed.

In both cases, the system to which a state is assigned doesn't exist. Hence the assignment is scientifically meaningless. It is like assigning properties to a unicorn.

2. As I say, this was intended to tease out your viewpoint on the Delayed Choice Entanglement Swap. I want to make sure I have your perspective correct, so please help me along here: In your view (paraphrasing): "Photons 1 & 4 are never 'dynamically' entangled into a true Bell state. That's because photons cannot be entangled after they cease to exist." Your viewpoint would then demonstrate a consistent application of that idea between the Megidish 2012 paper (Never Co-exist) and the Ma 2012 paper (Delayed Choice).

See my comment above.

yours is a denial of the conclusions of all Delayed Choice Experiments - Entanglement Swapping, MZI variants, or whatever.

No. I deny nothing. I only emphasize that the interpretation given to these experiments is not backed by theory. If there were theory you would have pointed to it by now.

They all create some kind of quantum state due to some future (or alternative) action being performed.

They create statistics, not states! Their states are already determined by the standard quantum evolution of their experimental setup, and they all have definite times! No matter which as-if states are promoted by words without a theoretical justification.

Again, there are interpretations of QM that explain these phenomena in various manners, and if you are using your preferred interpretation (I assume the Thermal Interpretation) then that is an "out".

My claim that there is no backup by theory is interpretation independent.

a. "If instead Photons 2 and 3 had been measured directly"? Especially curious about "directly".

Without putting them through the half-silvered mirror = what you call the non-swapping choice.

b. "only one of the choices was discussed and actualized, and the other suppressed"? Especially curious about "suppressed".

suppressed = neither performed nor its possibility discussed, although they could have done it, as in the references [21,22] they refer to at the top of the left column under Figure 2:

Recently, entanglement swapping was demonstrated with a delayed choice, where all four photons were created simultaneously, but photons 1 and 4 were measured before a choice had been made whether to entangle them or not [21, 22].

They report about delayed choice experiment, and deliberately made their experiment different by not allowing a choice - that could have easily be made (and then would have been delayed) by a straightforward modification of their setup.

All of the delayed choice experiments I cite show both the statistics for the swapping choice (creating a Bell state for 2 & 3) and the non-swapping choice (creating a Product state for 2 & 3).

Yes, and the authors of the paper under discussion could have done so as well, then it would have been a delayed choice experiment. But they needed to be different (else their result could not have been sold as exciting...)

c. Not entirely sure which experiment/references you mean "[21, 22]". I checked both papers and could not fit them to what you said.

I hadn''t check the papers but simply assumed that their remark (quoted above) summarized correctly these references. The only point of mentioning [21,22] was to point out that they knew about delayed choice experiments similar to their own experiment, and that they could have designed their experiment as a delayed choice experiment, too, but had reasons not to do so.

 

[Morbert]

No. The $\tau$-labelled states are temporal modes, hence have no interpretation as dynamical states.

What I am wondering is if, using your terminology, a "fictitious state" is just an expansion of a "real state" in a time-bin basis, like equation (5) in this paper, and hence subject to dynamics as per usual. i.e.
$$U|\Psi\rangle = \sum_jc_jUA^\dagger_j|0\rangle$$where the lhs is "real" and the rhs is a linear combination of "fictitious" temporal modes.

 

[PeterDonis]

if, using your terminology, a "fictitious state" is just an expansion of a "real state" in a time-bin basis

No, it isn't, because any "real" state by the definition @A. Neumaier gave only has kets that all refer to the same time. There's no way to rearrange such a state to include kets that refer to different times.

 

[DrChinese]

No, he is just applying non-relativistic QM in a domain in which everyone, including @DrChinese, agrees that it works. ... any talk about any states involving kets at different times, as in the papers under discussion, cannot be justified by NRQM.

This is not a question of what words to use. If someone wants to call Bell states with kets at different times "entangled", that's a matter of words, not physics. But if someone wants to claim that such states are "real"--and @DrChinese has explicitly said in this thread that he is making that claim, and that he thinks the authors of the papers he has referenced are making that claim too--then they should be able to justify that claim with something more than just the assertion that, since the Bell states make the correct predictions, they must be real.

Of course there is no question about the predictions of NRQM, everyone agrees on these - fortunately!

And there is no question that every reference on Delayed Choice Entanglement Swapping refers to it in the same way, which is as I do. That's a *large* body of (wrong?) work. And they all follow the same NRQM. I'm pretty sure they well understand the Schrödinger equation and its time parameter.

Below, a diagram associated with the 2022 Nobel for Physics on entanglement phenomena (from the Royal Swedish Academy of Sciences*). Note that there is no mention that the 1 & 4 photons need to be measured at any particular time relative to the execution of the Entangler for them to become entangled. That's because there is no such requirement. In the words of Ma, Zotter, Kofler, Ursin, Jennewein, Brukner, and Zeilinger: "Using four photons, we can actively delay the choice of measurement – implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator – on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as 'quantum steering into the past'."

Is this a difference in semantics? I'm not particularly disagreeing with that assessment**. Certainly, Quantum Interpretations tend to come to the foreground in these discussions, even if we are not explicitly discussing those in this context.

*Known for the rapid speed at which they award prizes for novel work.
** And if it is, I don't think I am in the smaller boat.

 

[mattt]

Of course there is no question about the predictions of NRQM, everyone agrees on these - fortunately!

And there is no question that every reference on Delayed Choice Entanglement Swapping refers to it in the same way, which is as I do. That's a *large* body of (wrong?) work. And they all follow the same NRQM. I'm pretty sure they well understand the Schrödinger equation and its time parameter.

Below, a diagram associated with the 2022 Nobel for Physics on entanglement phenomena (from the Royal Swedish Academy of Sciences*). Note that there is no mention that the 1 & 4 photons need to be measured at any particular time relative to the execution of the Entangler for them to become entangled. That's because there is no such requirement. In the words of Ma, Zotter, Kofler, Ursin, Jennewein, Brukner, and Zeilinger: "Using four photons, we can actively delay the choice of measurement – implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator – on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as 'quantum steering into the past'."

Is this a difference in semantics? I'm not particularly disagreeing with that assessment**. Certainly, Quantum Interpretations tend to come to the foreground in these discussions, even if we are not explicitly discussing those in this context.


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*Known for the rapid speed at which they award prizes for novel work.
** And if it is, I don't think I am in the smaller boat.

Your interpretation of their wording (in the case I refer to) IS incompatible with NRQM. You are NOT using NRQM to explain the results, because your explanation invokes "states" that don't exist in NRQM.

 

[DrChinese]

Without putting them through the half-silvered mirror = what you call the non-swapping choice.

suppressed = neither performed nor its possibility discussed, although they could have done it, as in the references [21,22] they refer to at the top of the left column under Figure 2:

They report about delayed choice experiment, and deliberately made their experiment different by not allowing a choice - that could have easily be made (and then would have been delayed) by a straightforward modification of their setup.

I believe you have misread the results. The Ma (2012) and Megidish (2012) experiments both show the statistics when there is a choice made to swap, versus when the choice is made not to swap. A time delay for one path, or other method to distinguish the sources, is the difference. The statistics change as would be expected by theory. See table 1 (page 12) in the Ma experiment, and figure 3 (page 4) in the Megidish experiment. I can cite the specific numbers if you like.

 

[PeterDonis]

I'm pretty sure they well understand the Schrödinger equation and its time parameter.

We are going around in circles. Basically you are saying that (1) the authors of the paper are authorities, so we should accept without question whatever they say, and (2) your interpretation of what they say, which entails the claim you have made about Bell states involving photons that never coexist being "real", is obviously correct and we have no valid reason to question it.

At least three others in this thread (myself, @A. Neumaier and @mattt) do not accept either of those statements. So just continuing to repeat them and add more quotes from more papers that say the same things gets us nowhere. If you cannot actually address the substance of our counterarguments in any other way, this thread has run its course and we might as well close it.

 

[DrChinese]

Your interpretation of their wording (in the case I refer to) IS incompatible with NRQM. You are NOT using NRQM to explain the results, because your explanation invokes "states" that don't exist in NRQM.

You are around 20 years behind the community. How you present the 1927 Schrödinger equation (i.e. prior to the discovery of entanglement) does not change the consensus today. Because these entangled Bell states have been discussed for a long time in the manner I describe, and in the delayed choice math I have presented, going back at least to Peres (1999) and Jennewein et al (2002).

Again: all you need to do is present a recent contrary peer-reviewed reference to convince anyone (including me) otherwise. Doesn't it make you wonder why such a reference seems to be missing for your perspective, while apparently there are no shortage of references supporting what I say? (As included in the post you are replying to.)

My references are not proof of the correctness of what I claim. But they are proof that the physics community consensus is as I describe (and as I claim). They can all still be wrong, and you could still be right - no argument from me. So your simple acknowledgement of these facts is in order. You are the one out of sync with generally accepted physics.

 

[mattt]

You are around 20 years behind the community. How you present the 1927 Schrödinger equation (i.e. prior to the discovery of entanglement) does not change the consensus today. Because these entangled Bell states have been discussed for a long time in the manner I describe, and in the delayed choice math I have presented, going back at least to Peres (1999) and Jennewein et al (2002).

Again: all you need to do is present a recent contrary peer-reviewed reference to convince anyone (including me) otherwise. Doesn't it make you wonder why such a reference seems to be missing for your perspective, while apparently there are no shortage of references supporting what I say? (As included in the post you are replying to.)

My references are not proof of the correctness of what I claim. But they are proof that the physics community consensus is as I describe (and as I claim). They can all still be wrong, and you could still be right - no argument from me. So your simple acknowledgement of these facts is in order. You are the one out of sync with generally accepted physics.

Your answer is really strange. NRQM explains all these experiments just fine.

It is your wording what is not backed up by NRQM.

 

[DrChinese]

1. We are going around in circles. Basically you are saying that (1) the authors of the paper are authorities, so we should accept without question whatever they say, and (2) your interpretation of what they say, which entails the claim you have made about Bell states involving photons that never coexist being "real", is obviously correct and we have no valid reason to question it.

2. At least three others in this thread (myself, @A. Neumaier and @mattt) do not accept either of those statements. So just continuing to repeat them and add more quotes from more papers that say the same things gets us nowhere. If you cannot actually address the substance of our counterarguments in any other way, this thread has run its course and we might as well close it.

1. You have a reason to question it. And yes, the authors *are* authorities. But that does not make them automatically correct. You could acknowledge that your view is out of sync with those authorities without any inconsistency. Do you believe your own viewpoint? If so, accept that you are out of step with the community. You wouldn't be the first.

2. I stepped away from the Megidish paper precisely because you three questioned its results. I re-focused on the Ma paper because I thought that had more authoritative weight within the community, and might be easier to discuss. Apparently, no evidence is adequate here if it differs from what you believe - even the words of highly respected teams.

If you think those following this thread are NOT learning (or otherwise gaining) from the references and quotes I provide: then I don't object to any decision you make as a moderator about closing it.

But: I do think you are biased in your presentations in this thread in favor your own viewpoint (i.e. not as a moderator). I say that precisely because I have provided authoritative citations, and no one (including you) else has; and yet you question whether my perspective matches scientific consensus. Clearly, mine does; and yet you easily dismiss both quoted consensus and my presentation of same. Are you being objective?

While your experience here dwarfs mine, I have never seen that from any other moderator in any other thread - in QM or anywhere here. So I would ask you to re-consider the full value of the citations I have provided. If after that, you think the thread has no ongoing utility, then the decision to close is yours to make without objection from me.

 

[DrChinese]

Your answer is really strange. NRQM explains all these experiments just fine.

It is your wording what is not backed up by NRQM.

I am quoting papers by a Nobel prize winner, who is describing standard contemporary QM. Seriously, doesn't it seem strange that you aren't - and I am? What's ambiguous here? Delayed choice entanglement swapping:

"Using four photons, we can actively delay the choice of measurement – implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator – on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as 'quantum steering into the past'."

 

[mattt]

But DrChinese, your description of the situation in this thread is not accurate.

Peter, Arnold and myself are using the proper mathematics of NRQM to support everything we say.

You are not doing the same. You only present some fictional mathematical symbols, that supposedly represent a "state" that doesn't exist in NRQM, and pretend that everything is OK (an attitude that is quite surprising to me, by the way).

Another strange thing is your tendency to constantly misrepresent what other posters are writing. For example more than once you were trying to suggest that Arnold or I were disputing those experimental results. That was never true. Or that we said that NRQM could not explain them. Never true again.

This causes more repetition than necessary, because we then feel obligued to state that we never implied those things, and the thread goes on and on in circles, when it could have ended had you addressed the only thing we were asking for: "a theoretical, mathematical explanation of those states within the mathematics of NRQM".

Obviously there is a huge asymmetry in the solidness of the different reasonings here.

By the way, I say all this with all my respect to you and anyone else. I love to talk about Physics and Mathematics, but I think it is sad when very interesting threads turn at the end in a succession of pointless repetitions.

English is neither my first nor my second language, so I hope I didn't sound harsh or inappropiate.