Photons from separated sources can be entangled - after they were detected

[DrChinese]

DrChinese: Are you SURE you don't secretly want to make kissy-poos with the Transational Interpreation? The atemporal aspects would seem right up your alley. ;)

Aw shucks, I love 'em all!

 

[SpectraCat]

The interesting thing about the collapse issue is that you really cannot explicitly determine that the first measurement caused the collapse. It could have been the other way around, but we assign causality to coincide with a single direction in time. (I personally use the term "as if" often because it is a simple and easy rule to remember, i.e. it is "as if" the first measurement causes the collapse.) As far as I know: there is no evidence whatsoever for idea that entanglement ends for Alice when Bob is first measured as opposed to vice versa (i.e. that it is in fact Alice that causes the collapse). Certainly, the DCQE experiments don't show anything like that. I think that point would be one which is pretty important. This nuance is what brings out the significance of the term "contextual". You consider the entire relevant context, whatever that happens to be.

Actually, I have studied this issue pretty intensely over the last few weeks, and while my readings have been far from comprehensive, I have not found a single example of an experiment that supports your claim that causality is not restricted to the foward direction in time. In all the examples I have seen, there has never been an example where data recorded in the past has been changed by an event that occurred later in time. I have seen lots of claims and smoke and mirrors, but upon a careful reading, the "choice" event always temporally precedes or coincides with the measurements that are dependent on the result of the choice. DCQE (delayed choice quantum eraser) experiments, at least the ones I have seen reported in peer-reviewed journals, always fall into this category. I would very much like to see a DCQE experiment that actually shows a Bell's inequality violation for data that was detected before the DC event occurred.

So anyway, I am not buying the whole future affects the past thing until I see a more convincing experiment. The one that we laid out and debated early in this thread would certainly qualify. I hope someone does it soon.

Again, to quote Zeilinger et al: "Therefore, this result indicate that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres: this paradox does not arise if the correctness of quantum mechanics is firmly believed." They specifically refer to this as a delayed choice experiment.

Yeah .. that sounds like doctrine to me, or maybe dogma, but I don't agree that it is a scientific conclusion that follows from the results of that particular paper. I *do* believe in the correctness of QM, that is not at issue here. I have a problem seeing the paradoxes that people refer to in statements like the one from your quote above, because I haven't yet seen any evidence, or even a convincing gedanken experiment, that shows that "the time ordering of the detection events has no influence on the results". So maybe I just don't understand the underlying physics well enough yet, but I kinda doubt it, and it is certainly not for lack of trying ...

 

[Frame Dragger]

Actually, I have studied this issue pretty intensely over the last few weeks, and while my readings have been far from comprehensive, I have not found a single example of an experiment that supports your claim that causality is not restricted to the foward direction in time. In all the examples I have seen, there has never been an example where data recorded in the past has been changed by an event that occurred later in time. I have seen lots of claims and smoke and mirrors, but upon a careful reading, the "choice" event always temporally precedes or coincides with the measurements that are dependent on the result of the choice. DCQE (delayed choice quantum eraser) experiments, at least the ones I have seen reported in peer-reviewed journals, always fall into this category. I would very much like to see a DCQE experiment that actually shows a Bell's inequality violation for data that was detected before the DC event occurred.

So anyway, I am not buying the whole future affects the past thing until I see a more convincing experiment. The one that we laid out and debated early in this thread would certainly qualify. I hope someone does it soon.




Yeah .. that sounds like doctrine to me, or maybe dogma, but I don't agree that it is a scientific conclusion that follows from the results of that particular paper. I *do* believe in the correctness of QM, that is not at issue here. I have a problem seeing the paradoxes that people refer to in statements like the one from your quote above, because I haven't yet seen any evidence, or even a convincing gedanken experiment, that shows that "the time ordering of the detection events has no influence on the results". So maybe I just don't understand the underlying physics well enough yet, but I kinda doubt it, and it is certainly not for lack of trying ...

It sounds to me like your understanding is just fine, but you choose to reject all of the Interpretations of QM. You're concerned with the utility of QM, and the reality of something requires some evidence to satisfy you. You accept theories based on their predictive qualities, but you don't believe they are accurate or complete descriptions of nature. I don't think you'll get much argument here, at least, not from me. Interpretations are just lenses through which to consider the apparently paradoxical nature in some elements of QM.

Determinism, or Uncertainty... I don't find either comforting, and I am willing to believe that nature as a whole is mostly unlike we percieve it on a daily basis. That said, like you, I want to see some evidence before I start questioning my worldview(s) and a universal history of a single arrow of time.

 

[Demystifier]

No, I agree that it takes classical communication to make sense of the bits of information lying around at different places. But don't think I don't look for something anyway! I love to dream up FTL setups just to shoot them down. That is how this thread started!

Now you confused me. At the moment, do you or do you not think that your setup can be used to send information to the past?

 

[zonde]

Sure, here is a diagram which shows what I am referring to, and a reference to where it originated:

http://www.pas.rochester.edu/~AdvLab/Eberly_Bell_Inequalities_AJP.pdf

"We employ an arrangement of polarization analyzer loops to derive several simple Bell inequalities and then discuss the violation of one of them in light of quantum and classical interpretations of the data recorded."

This is definitely not relevant to BSM!
Simply count the inputs.
BSM - 2 inputs, 2 outputs
This example - 1 input, 2 outputs that are then recombined into 1 output again.

Yet another difference is that in this example beam is split using PBSes but BSM is done using polarization independent BS.

 

[Matterwave]

Now you confused me. At the moment, do you or do you not think that your setup can be used to send information to the past?

If I've understood Dr. Chinese's argument correctly (which, I'm not sure I did =P), he believes this experiment can send information to the past only in the sense that entanglement can send information from one particle to another (making sure the pairs are anti-correlated).

No real information can be sent without a classical means of communication. I think, just as in the normal Bell tests, one can't tell if his particle's entangled pair was detected or not because either way, it looks random to him (until he compares notes with his partner).

 

[peteratcam]

There seems to be disagreement on what a BSM is in this thread. In the context of this discussion, should I understand a 'Bell State Measurement' to be a measurement which distinguished between the 4 'maximally entangled' states. eg, a measurement of the operator
[tex]\sigma^x_1\sigma^x_2 + 2\sigma^z_1\sigma^z_2[/tex]
which it can be checked has 4 distinct eigenvalues, with the maximally entangled states as eigenvectors.

Thanks.

 

[Demystifier]

If I've understood Dr. Chinese's argument correctly (which, I'm not sure I did =P), he believes this experiment can send information to the past only in the sense that entanglement can send information from one particle to another (making sure the pairs are anti-correlated).

No real information can be sent without a classical means of communication. I think, just as in the normal Bell tests, one can't tell if his particle's entangled pair was detected or not because either way, it looks random to him (until he compares notes with his partner).

OK, that means that we can agree now that information cannot be sent to the past in any practical sense and that it does not depend on the interpretation.

However, we still have an unanswered question: What happens at the fundamental microscopic level? Can information be sent to the past at THIS level? Unfortunately, this question cannot be answered without referring to any particular interpretation. Therefore, I will answer this question from the point of view of MWI/BI, which are sufficiently similar to provide a common answer for both interpretations. According to these interpretations, nature is DETERMINISTIC at the microscopic level. Therefore, there is no free will (except as an illusion). Therefore, Charlie does not have a free choice to do what he wants. Instead, the Charlie's action is predetermined by conditions present at the time at which Alice and Bob made their measurements (or even earlier). Therefore there is no reason to interpret the correlations as sending microscopic information to the past. Thus, MWI/BI deals with it quite well and there is no particular preference for introducing transactional interpretation. Q.E.D.

 

[Zarqon]

Not sure if I missed something since I just quickly read through the whole thread, but I noted DrChinese mentioning quantum repeaters several times, and I just wish to make a point about this that might clear things up.

In the case of quantum repeaters where you extend the chain of entangled photons to many pairs, it is imperative that the photons are stored in a quantum memory in the intermediate steps, during the time the entanglement swapping measurements (BSMs) are done, otherwise there will not be any coherence left to keep extending the chain. I got the impression that you are talking about photon A and D being "measured" to find entanglement, and surely this measurement corresponds to decoherence of the quantum states, and the photon pairs would not be valid for use in further quantum repeater chains.

I think this might solve the confusion, because I think DrChinese's setup from the original post will only work if the photons A and D are stored in quantum memories, then they can become entangled at any point as soon as Charlie decides to make his swapping. If at anytime before the swapping operation, you would measure the polarization state of A and D (regardless of whether you measure the photon directly or the equivalent state stored in the quantum memory), you would never be able to entangle them.

Also, the change to the quantum state stored in the quantum memory after the BSM, does not violate any causality, since you have to first receive classical information from Charlie on the outcome of the BSM, before you can know what basis to measure the quantum state in, i.e. in what basis the entanglement can be detected.

I hope I understood the problem correctly.

 

[DrChinese]

Now you confused me. At the moment, do you or do you not think that your setup can be used to send information to the past?

I absolutely do not believe that a) information can be sent to the past, nor do I believe that b) information can be sent faster than light (FTL). I hope that is clear

To me, a) and b) are the same restriction. It seems whenever you get close to finding a "loophole" in the no-signaling rule, QM pops up with some funny detail and the "information" you want to send is simply encoded as a random series of bits that requires another key to decode. (That is what quantum communication is all about anyway, isn't it?)

 

[SpectraCat]

Not sure if I missed something since I just quickly read through the whole thread, but I noted DrChinese mentioning quantum repeaters several times, and I just wish to make a point about this that might clear things up.

In the case of quantum repeaters where you extend the chain of entangled photons to many pairs, it is imperative that the photons are stored in a quantum memory in the intermediate steps, during the time the entanglement swapping measurements (BSMs) are done, otherwise there will not be any coherence left to keep extending the chain. I got the impression that you are talking about photon A and D being "measured" to find entanglement, and surely this measurement corresponds to decoherence of the quantum states, and the photon pairs would not be valid for use in further quantum repeater chains.

I think this might solve the confusion, because I think DrChinese's setup from the original post will only work if the photons A and D are stored in quantum memories, then they can become entangled at any point as soon as Charlie decides to make his swapping. If at anytime before the swapping operation, you would measure the polarization state of A and D (regardless of whether you measure the photon directly or the equivalent state stored in the quantum memory), you would never be able to entangle them.

Also, the change to the quantum state stored in the quantum memory after the BSM, does not violate any causality, since you have to first receive classical information from Charlie on the outcome of the BSM, before you can know what basis to measure the quantum state in, i.e. in what basis the entanglement can be detected.

I hope I understood the problem correctly.

I think you did understand it correctly, and your analysis agrees with that of myself and DeMystifier, although I for one am not completely familiar with the concept of quantum memory. Is that equivalent to "persistence of an entangled state"? Stated another way, can we consider two entangled photons propagating along their respective beamlines in an unperturbed state to be "in quantum memory"?

 

[Frame Dragger]

I absolutely do not believe that a) information can be sent to the past, nor do I believe that b) information can be sent faster than light (FTL). I hope that is clear

To me, a) and b) are the same restriction. It seems whenever you get close to finding a "loophole" in the no-signaling rule, QM pops up with some funny detail and the "information" you want to send is simply encoded as a random series of bits that requires another key to decode. (That is what quantum communication is all about anyway, isn't it?)

Yes, to your last question. The main attraction is being tamper-evident in ANY circumstance. That would be a radical leap in crytoplogy and the handling of information, and depending on the cost there is no telling whether this would create an elite with perfectly secure coms, or give ultimate security to the masses?! I don't even know which is a better idea!

 

[SpectraCat]

OK, that means that we can agree now that information cannot be sent to the past in any practical sense and that it does not depend on the interpretation.

However, we still have an unanswered question: What happens at the fundamental microscopic level? Can information be sent to the past at THIS level? Unfortunately, this question cannot be answered without referring to any particular interpretation. Therefore, I will answer this question from the point of view of MWI/BI, which are sufficiently similar to provide a common answer for both interpretations. According to these interpretations, nature is DETERMINISTIC at the microscopic level. Therefore, there is no free will (except as an illusion). Therefore, Charlie does not have a free choice to do what he wants. Instead, the Charlie's action is predetermined by conditions present at the time at which Alice and Bob made their measurements (or even earlier). Therefore there is no reason to interpret the correlations as sending microscopic information to the past. Thus, MWI/BI deals with it quite well and there is no particular preference for introducing transactional interpretation. Q.E.D.

Wait, what? It now sounds like you have reversed yourself and now expect there to be a Bell's inequality violation for Alice and Bob's results, based on Charlie's future choice? Isn't that different from your earlier arguments about the decoherence of the initial entangled pairs (A/B) and (C/D) caused by Alice and Bob's measurements precluding the possibility that there A & D could be entangled "after the fact", as originally proposed by Dr. Chinese?

 

[DrChinese]

Not sure if I missed something since I just quickly read through the whole thread, but I noted DrChinese mentioning quantum repeaters several times, and I just wish to make a point about this that might clear things up.

In the case of quantum repeaters where you extend the chain of entangled photons to many pairs, it is imperative that the photons are stored in a quantum memory in the intermediate steps, during the time the entanglement swapping measurements (BSMs) are done, otherwise there will not be any coherence left to keep extending the chain. I got the impression that you are talking about photon A and D being "measured" to find entanglement, and surely this measurement corresponds to decoherence of the quantum states, and the photon pairs would not be valid for use in further quantum repeater chains.

I think this might solve the confusion, because I think DrChinese's setup from the original post will only work if the photons A and D are stored in quantum memories, then they can become entangled at any point as soon as Charlie decides to make his swapping. If at anytime before the swapping operation, you would measure the polarization state of A and D (regardless of whether you measure the photon directly or the equivalent state stored in the quantum memory), you would never be able to entangle them.

I disagree, there is no mention of "holding" A & D in Zeilinger's published version of the experiment with delayed choice - nor would there need to be for the effect to appear. The entire point of all delayed choice experiments is that it appears "as if" the past was changed by a future choice. However, the histories are always "consistent" when all the facts are brought together. So it is not clear that any particular portion of the setup "caused" the outcome. That is why QM can be labeled "indeterministic" as much as the fact that there is no apparent cause for the particular outcome. (Caveat: As always, such labels are interpretation dependent.)

See the attached figures 1 and 2 from the reference itself.

The issue of quantum repeaters is a little different. There is no requirement that the information be held in a quantum memory for the entanglement swapping to work per se, but that may not lead to a working repeater. I believe, as best as can be determined, the issue has to do with the practicality of synchronizing so many photon pairs over large distances. If you cannot have pairs readily available when you need them, the repeater won't do anything useful. Also, the repeater must repeat with a known Bell state and this leads to additional complexity. There are also fidelity issues of a variety of types as you might imagine.

 

[Frame Dragger]

I disagree, there is no mention of "holding" A & D in Zeilinger's published version of the experiment with delayed choice - nor would there need to be for the effect to appear. The entire point of all delayed choice experiments is that it appears "as if" the past was changed by a future choice. However, the histories are always "consistent" when all the facts are brought together. So it is not clear that any particular portion of the setup "caused" the outcome. That is why QM can be labeled "indeterministic" as much as the fact that there is no apparent cause for the particular outcome. (Caveat: As always, such labels are interpretation dependent.)

See the attached figures 1 and 2 from the reference itself.

The issue of quantum repeaters is a little different. There is no requirement that the information be held in a quantum memory for the entanglement swapping to work per se, but that may not lead to a working repeater. I believe, as best as can be determined, the issue has to do with the practicality of synchronizing so many photon pairs over large distances. If you cannot have pairs readily available when you need them, the repeater won't do anything useful. Also, the repeater must repeat with a known Bell state and this leads to additional complexity. There are also fidelity issues of a variety of types as you might imagine.

This strikes me as an experiment that would require vast resources to build, calibrate, and perform with fidelity. Is it even possible with current technology to build this such that it yields a result worth the building expense?

 

[DrChinese]

This strikes me as an experiment that would require vast resources to build, calibrate, and perform with fidelity. Is it even possible with current technology to build this such that it yields a result worth the building expense?

Sure, there are quite a number of labs doing this research - and they are pushing the boundaries all the time. The experiment I cite was from 2002 (practically ancient now), and labs have been churning out groundbreaking experiments since. Some of the key reseachers are (with my sincere apologies to the many many! many! others who are also active):

Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, and Anton Zeilinger at the University of Austria

Nicolas Sangouard, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin at the University of Geneva

Harald Weinfurter at the Max Planck Institute for Quantum Optics

Artur Scherer, Gina Howard, Barry C. Sanders, and Wolfgang Tittel at the Institute for Quantum Information Science, University of Calgary

I mention the above specifically because when you see their names as authors, you will know they are working as part of some of these major lab efforts.

Now, if you are referring to the repeaters specifically: here are 2 recent and very comprehensive theoretical works which summarize a lot of the complexities involved. Each is over 50 pages:

http://arxiv.org/abs/0906.2699

http://arxiv.org/abs/0807.3358

 

[Frame Dragger]

Sure, there are quite a number of labs doing this research - and they are pushing the boundaries all the time. The experiment I cite was from 2002 (practically ancient now), and labs have been churning out groundbreaking experiments since. Some of the key reseachers are (with my sincere apologies to the many many! many! others who are also active):

Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, and Anton Zeilinger at the University of Austria

Nicolas Sangouard, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin at the University of Geneva

Harald Weinfurter at the Max Planck Institute for Quantum Optics

Artur Scherer, Gina Howard, Barry C. Sanders, and Wolfgang Tittel at the Institute for Quantum Information Science, University of Calgary

I mention the above specifically because when you see their names as authors, you will know they are working as part of some of these major lab efforts.

Hmmmm... I wonder if they've considered this scenario? It always seems arrogant to assume they haven't, but then, what if you're on to something interesting? An email to the appropriate group might not be a bad idea.

 

[DrChinese]

If I've understood Dr. Chinese's argument correctly (which, I'm not sure I did =P), he believes this experiment can send information to the past only in the sense that entanglement can send information from one particle to another (making sure the pairs are anti-correlated).

No real information can be sent without a classical means of communication. I think, just as in the normal Bell tests, one can't tell if his particle's entangled pair was detected or not because either way, it looks random to him (until he compares notes with his partner).

Yes, that is exactly as I am trying to portray.

In a time symmetric interpretation (TS), you would be respecting c and could explain this result. In a Bohmian interpretation (BM), likewise. But what is interesting to me is that the standard QM interpretation (the SQM formalism) explains and predicts the entanglement swapping features, while neither TS or BM do. Now I realize my good friends with a BM or TS inclination will vigorously disagree, as they will point out complete equivalence to SQM. But in my opinion, the hoops required to explain entanglement swapping as described in my post 84 become increasing complex for mechanistic interpretations.

This is a point I have been trying to make for some time: that the Bell Theorem distinguished local realistic theories from other candidates (with LR losing). But more recent advances are serving to further narrow the crop of candidate theories (interpretations). Candidate interpretations that do not take these experimental challenges seriously are going to be left behind very quickly*. The researchers who are at the forefront of the advances in quantum communication/non-locality/contextuality - as far as I have read (which is hardly the final word!) - do not subscribe to any of the interpretations debated so vigorously on this board. They tend to stay very close to SQM at all times. This experiment is a perfect example.

* If they haven't already: because they are becoming even LESS useful for research purposes than they have been for the past 80 years.

 

[peteratcam]

The researchers who are at the forefront of the advances in quantum communication/non-locality/contextuality - as far as I have read (which is hardly the final word!) - do not subscribe to any of the interpretations debated so vigorously on this board. They tend to stay very close to SQM at all times. This experiment is a perfect example.

Indeed. I was at a seminar recently given by Anton Zeilinger where, in response to a question, he described Bohmian mechanics as a desperate attempt to maintain pre-quantum realism!
For completeness, I should say he gestured quotation marks for the word 'desperate'.

 

[DrChinese]

Indeed. I was at a seminar recently given by Anton Zeilinger where, in response to a question, he described Bohmian mechanics as a desperate attempt to maintain pre-quantum realism!
For completeness, I should say he gestured quotation marks for the word 'desperate'.

Thanks for sharing that story! Got any more good ones?

(All of the written articles are generally devoid of humor or opinion, so I am always trying to read between the lines to get an idea of the personality behind the names.)

 

[Frame Dragger]

The discussion of Interpretations is fun, because it's metaphysics. We could argue as to the value of the view you take, but ultimately being free of any agenda (Instrumentalism) is where the progress comes from. The rest is meant to explain the seemingly inexplicable to we poor fur-less apes.

 

[SpectraCat]

The discussion of Interpretations is fun, because it's metaphysics. We could argue as to the value of the view you take, but ultimately being free of any agenda (Instrumentalism) is where the progress comes from. The rest is meant to explain the seemingly inexplicable to we poor fur-less apes.

Not always metaphysical .. LHV interpretations were once seriously considered on equal footing with SQM. Now they are considered to be wrong. So, arguing about interpretations is fun for its own sake, but I suspect it's even more fun when you get to blow a hole in one of them and sink it!

 

[Frame Dragger]

Not always metaphysical .. LHV interpretations were once seriously considered on equal footing with SQM. Now they are considered to be wrong. So, arguing about interpretations is fun for its own sake, but I suspect it's even more fun when you get to blow a hole in one of them and sink it!

It's so fun that we have the LHC to whack these theories around with. Just think, if you'd been born a few hundred, or god forbid a few THOUSAND years ago you'd be missing all of this!

 

[Demystifier]

I absolutely do not believe that a) information can be sent to the past, nor do I believe that b) information can be sent faster than light (FTL). I hope that is clear

To me, a) and b) are the same restriction.

They are not exactly the same. If you could invert the thermodynamic arrow of time, then you could send information to the past without FTL.

 

[Demystifier]

Wait, what? It now sounds like you have reversed yourself and now expect there to be a Bell's inequality violation for Alice and Bob's results, based on Charlie's future choice? Isn't that different from your earlier arguments about the decoherence of the initial entangled pairs (A/B) and (C/D) caused by Alice and Bob's measurements precluding the possibility that there A & D could be entangled "after the fact", as originally proposed by Dr. Chinese?

You should distinguish macroscopic and microscopic levels of description. My previous explanations referred to macroscopic phenomena, while the one you are citing above refers to microscopic phenomena. In particular, free will and decoherence make sense only at a macroscopic level.

 

[DrChinese]

Originally Posted by DrChinese

I absolutely do not believe that a) information can be sent to the past, nor do I believe that b) information can be sent faster than light (FTL). I hope that is clear

To me, a) and b) are the same restriction.

Demystifier:
They are not exactly the same. If you could invert the thermodynamic arrow of time, then you could send information to the past without FTL.

Sorry, I did not express myself well. I meant to imply that both of these restrictions (which as you say are not identical) arise from the same source. Whatever that is... as it seems that the same barrier exists whether you are trying to send information to the past or whether you are trying to send information FTL. You still need classical channels to make sense of the otherwise random bits you are holding. And that's all you can ever send through the various forms of entanglement/delayed choice/etc: Random bits.

 

[SpectraCat]

You should distinguish macroscopic and microscopic levels of description. My previous explanations referred to macroscopic phenomena, while the one you are citing above refers to microscopic phenomena. In particular, free will and decoherence make sense only at a macroscopic level.

So I am confused, do you expect a Bell's inequality violation for photons A & D when Charlie makes his BSM on B & C *after* the detection of A & D, or don't you? And in this case, we are talking about 4-way coincidence measurements (with appropriate consideration of travel delays) on A,B,C and D, right?

Also, I am a little unclear on the distinction you are drawing between microscopic and macroscopic phenomena ... are you saying Bell's inequality violations are microscopic?

 

[Frame Dragger]

So I am confused, do you expect a Bell's inequality violation for photons A & D when Charlie makes his BSM on B & C *after* the detection of A & D, or don't you? And in this case, we are talking about 4-way coincidence measurements (with appropriate consideration of travel delays) on A,B,C and D, right?

Also, I am a little unclear on the distinction you are drawing between microscopic and macroscopic phenomena ... are you saying Bell's inequality violations are microscopic?

I have been under the impression that the line between 'micro' and 'macro' in QM is (forgive me) fuzzy. Isn't the notion of where and when macroscopic reality emerges from quantum behaviour one of the bigger unsolved questions of any interpretation of QM?

 

[Demystifier]

I have been under the impression that the line between 'micro' and 'macro' in QM is (forgive me) fuzzy. Isn't the notion of where and when macroscopic reality emerges from quantum behaviour one of the bigger unsolved questions of any interpretation of QM?

I think that decoherence defines the boundary quite well. The boundary is not sharp (there are also mesoscopic systems), but even the "unsharpness" can be well defined in terms of decoherence.

 

[Demystifier]

So I am confused, do you expect a Bell's inequality violation for photons A & D when Charlie makes his BSM on B & C *after* the detection of A & D, or don't you?

I do expect Bell's inequality violation in this case. (Note that this was not my opinion in the beginning. I can make a mistake too.) However, Alice and Bob cannot observe them. Only Charlie can.

And in this case, we are talking about 4-way coincidence measurements (with appropriate consideration of travel delays) on A,B,C and D, right?

Right! That's why Alice and Bob cannot observe it.

Also, I am a little unclear on the distinction you are drawing between microscopic and macroscopic phenomena ... are you saying Bell's inequality violations are microscopic?

No, we can observe them so they are macroscopic. Microscopic stuff is something that we cannot directly observe (e.g., Bohmian trajectories, objective wave functions, objective collapse, absence of any objective microscopic reality, ...) so at the moment we can only speculate about it.

 

[SpectraCat]

No, we can observe them so they are macroscopic. Microscopic stuff is something that we cannot directly observe (e.g., Bohmian trajectories, objective wave functions, objective collapse, absence of any objective microscopic reality, ...) so at the moment we can only speculate about it.

Ok, then I don't understand your comment about my previous post where you said that I needed to distinguish macroscopic with microscopic descriptions. All I mentioned in the post you quoted were Bell's Inequality violations and decoherence. But it doesn't really matter ... your position is clear to me now.

Incidentally, I still disagree (assuming I understand the situation correctly, which is something I am not completely sure about) ... I am working on a post to explain my (mis?) understanding in more detail

 

[DrChinese]

Incidentally, I still disagree (assuming I understand the situation correctly, which is something I am not completely sure about) ... I am working on a post to explain my (mis?) understanding in more detail

Really? I'm sitting in the bar waiting for my beers.

 

[SpectraCat]

Ok, so I have done some more reading and a lot more thinking about this, and I still can't understand how there can be any quantum teleportation if the entanglement of photons B & C occurs after A & D have been measured. This is *not* what was reported experimentally in this http://128.84.158.114/abs/quant-ph/0201134" (PRL 88, [2002] art. 017903) that we were discussing earlier. In that case, photons 1 & 2 (equivalent to B & C in Dr. Chinese's example) enter the fiber beam splitter and are entangled before 0 & 3 are measured. The only thing that is delayed is the measurement of the Bell state that 1 & 2 have been projected into, which does not reflect on the *fact* of their entanglement, only the measurement of the state. Dr. Chinese has claimed that this does not matter, and that the same teleportation would be observed if A & D are measured before B & C are entangled. I cannot see how this can be correct, and I have worked out some of my arguments mathematically below. Please let me know where my mistake lies, if there is one.

Paraphrasing equations 2 and 3 from the paper cited above, the total wavefunction is initially composed of two independent states, and can be written as:

[tex]\left|\Psi_{tot}\right\rangle = \left|\Psi^{-}_{AB}\right\rangle \otimes \left|\Psi^{-}_{CD}\right\rangle[/tex], where [tex]\left|\Psi^{-}_{xy}\right\rangle [/tex] refers to the Bell state,
[tex]\left|\Psi^{-}_{xy}\right\rangle = \frac{1}{\sqrt{2}}\left[\left|H\right\rangle_{x}\left|V\right\rangle_{y} - \left|V\right\rangle_{x}\left|H\right\rangle_{y}\right][/tex],
and H and V refer to orthogonal polarization states. [tex]\Psi_{tot}[/tex] can then be re-expressed in the basis of Bell states of the A/D and B/C pairs:

[tex]\left|\Psi_{tot}\right\rangle = \frac{1}{2}\left[\left|\Psi^{+}_{AD}\right\rangle \otimes \left|\Psi^{+}_{BC}\right\rangle - \left|\Psi^{-}_{AD}\right\rangle \otimes \left|\Psi^{-}_{BC}\right\rangle - \left|\Phi^{+}_{AD}\right\rangle \otimes \left|\Phi^{+}_{BC}\right\rangle + \left|\Phi^{-}_{AD}\right\rangle \otimes \left|\Phi^{-}_{BC}\right\rangle\right][/tex]

Therefore, at the moment when Charlie entangles B & C in his fiber beam splitter, the system is cast into one of the four states above, and this means that A & D must also be entangled. At some later point, the particular Bell state of B & C is measured at the detectors, and at that moment, Charlie knows which Bell state A & D are in as well.

This is all fine, but it only works if the first equation I wrote above is valid when B & C become entangled. This is not true if the measurements on A and D have already occurred. Immediately after those measurements have occurred, the total state of the system is known, that is, it has been resolved into some element of the set of separable states:

[tex]\left\{\left[\left|H\right\rangle_{A}\otimes\left|V\right\rangle_{B}\otimes\left|H\right\rangle_{C}\otimes\left|V\right\rangle_{D}\right],\:\:
\left[\left|V\right\rangle_{A}\otimes\left|H\right\rangle_{B}\otimes\left|H\right\rangle_{C}\otimes\left|V\right\rangle_{D}\right],\:\:
\left[\left|H\right\rangle_{A}\otimes\left|V\right\rangle_{B}\otimes\left|V\right\rangle_{C}\otimes\left|H\right\rangle_{D}\right],\:\:
\left[\left|V\right\rangle_{A}\otimes\left|H\right\rangle_{B}\otimes\left|V\right\rangle_{C}\otimes\left|H\right\rangle_{D}\right]\right\}[/tex]

(Note: I used the tensor product notation above to emphasize the separability, but it is just the 4 combinations: HVHV, VHHV, HVVH, VHVH)

So there is now no way to get from just one of these states to the case where there is entanglement between A & D. Note that B & C aren't entangled in this case either ... (otherwise it would be possible to generate entangled pairs from linearly polarized photons simply using beamsplitters).

Anyway, hopefully this makes my analysis and arguments clear. Have I made a deduction or math error somewhere? Note that at no point do I involve order of detection in my analysis, I only refer to the state of the system when the B & C photons enter the beamsplitter.

Finally, it is worth noting that in the paper I cited, the authors did not make the same claim that Dr. Chinese made in his post here. They claim that the space-time separation of the detection events doesn't matter, which is consistent with what they tested in their experiment.

 

[DrChinese]

... Finally, it is worth noting that in the paper I cited, the authors did not make the same claim that Dr. Chinese made in his post here. They claim that the space-time separation of the detection events doesn't matter, which is consistent with what they tested in their experiment.

Gee, I am not sure how much clearer they could have put it. And they come as close to the title of this thread as can be: "Photons from separated sources can be entangled - after they were detected!" I certainly get the feeling that you are going to great lengths to avoid buying a Cowboy fan a beer.

So here are the quotes, please reference again the attached diagram in Post 84. Those figures are from the Zeilinger article.

Article body:

"A seemingly paradoxical situation arises — as suggested by Peres [4] — when Alice’s Bellstate analysis is delayed long after Bob’s measurements. This seems paradoxical, because Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured. Nevertheless, quantum mechanics predicts the same correlations. Remarkably, Alice is even free to choose the kind of measurement she wants to perform on photons 1 and 2. Instead of a Bell-state measurement she could also measure the polarizations of these photons individually. Thus depending on Alice’s later measurement, Bob’s earlier results either indicate that photons 0 and 3 were entangled or photons 0 and 1 and photons 2 and 3. This means that the physical interpretation of his results depends on Alice’s later decision.

"Such a delayed-choice experiment was performed by including two 10 m optical fiber delays for both outputs of the BSA. In this case photons 1 and 2 hit the detectors delayed by about 50 ns. As shown in Fig. 3, the observed fidelity of the entanglement of photon 0 and photon 3 matches the fidelity in the non-delayed case within experimental errors. Therefore, this result indicate [sic] that the time ordering of the detection events has no influence on the results and strengthens the argument of A. Peres [4]: this paradox does not arise if the correctness of quantum mechanics is firmly believed."Figure 1: Shows diagram of setup.
"One photon from each pair is sent to Alice who subjects them to a Bell-state measurement, projecting them randomly into one of four possible entangled states. ... This procedure
projects photons 0 and 3 into a corresponding entangled state. [Bob] hands his results also to Victor, who sorts them into subsets according to Alice’s results, and checks each subset for a violation of Bell’s inequality. This will show whether photons 0 and 3 became entangled although they never interacted in the past. Interestingly, the quantum prediction for the observations does not depend on the relative space-time arrangement Alice’s and Bob’s detection events. "

Figure 3: Shows Fidelity, and Fidelity with Delayed Choice. [Note the words "delayed choice"]
"The square dots represent the fidelity for the case that Alice’s and Bob’s events are space-like separated, thus no classical information transfer between Alice and Bob can influence the results. The circular dot is the fidelity for the case, that Alice’s detections are delayed by 50 ns with respect to Bob’s detections. This means, that Alice’s measurement projects photon 0 and 3 in an entangled state, at a time after they have already been registered."

So can you point to any sentence above which makes you think that a) delayed choice version was not observed; b) entanglement did not occur; or c) the order of Alice and Bob's actions makes ANY difference to the outcome? Because it certainly seems clear to me. I don't even see in your analysis where the outcomes are different based on ordering.

 

[DrChinese]

...This is all fine, but it only works if the first equation I wrote above is valid when B & C become entangled. This is not true if the measurements on A and D have already occurred. Immediately after those measurements have occurred, the total state of the system is known, that is, it has been resolved into some element of the set of separable states:

[tex]\left\{\left[\left|H\right\rangle_{A}\otimes\left|V\right\rangle_{B}\otimes\left|H\right\rangle_{C}\otimes\left|V\right\rangle_{D}\right],\:\:
\left[\left|V\right\rangle_{A}\otimes\left|H\right\rangle_{B}\otimes\left|H\right\rangle_{C}\otimes\left|V\right\rangle_{D}\right],\:\:
\left[\left|H\right\rangle_{A}\otimes\left|V\right\rangle_{B}\otimes\left|V\right\rangle_{C}\otimes\left|H\right\rangle_{D}\right],\:\:
\left[\left|V\right\rangle_{A}\otimes\left|H\right\rangle_{B}\otimes\left|V\right\rangle_{C}\otimes\left|H\right\rangle_{D}\right]\right\}[/tex]

(Note: I used the tensor product notation above to emphasize the separability, but it is just the 4 combinations: HVHV, VHHV, HVVH, VHVH)

So there is now no way to get from just one of these states to the case where there is entanglement between A & D. Note that B & C aren't entangled in this case either ... (otherwise it would be possible to generate entangled pairs from linearly polarized photons simply using beamsplitters).

This analysis is just not true! The observation of A & D first changes nothing. You can see this is wrong quite easily. Just split the A & D observations into 2 separate events, which by your reasoning they now are. And let's consider ONLY the A & B case. According to you, A & B are now in a product state. But that is flat out incorrect, they are in the entangled state and produce statistics to match (assuming you measure B's polarization)!

Ditto with C & D. I hope you can see that the observation of A & D does NOT produce the state you describe above UNTIL, and UNLESS, and AFTER the polarizations of B & C are also measured. Which in the Zeilinger experiment they are NOT, because a Bell State Measurement is performed instead. Due to the BSM, regardless of when it occurs, A & D are projects into an entangled state and this is what is shown to violate a Bell Inequality in their Figure 3.

In reality, the context of the A & B pair measurement and the context of the C & D pair measurement is critical. CONTEXT is always critical, and must be considered carefully. Although we talk about collapse as if it is instantaneous, it really transcends that description. It cannot strictly be said to occur upon first measurement. Otherwise, the observation of the second member of an entangled pair would not lead to the violation of a Bell Inequality (because then they would be separated once the entanglement is collapsed).