Flaw in Anton Zeilinger QM entanglement article

[RandallB]

Flaw in Anton Zeilinger article (Rev. Mod. Phys., Vol. 71, No. 2, Centenary 1999)

This Thread is a continuation from the “Cramer new experiment” thread (see DrC post origin) to separate out comments on an Anton Zeilinger article from the discussion on Cramer ‘Transactional Interpretation’ & "retrocausality".

an enlightening article by Anton Zeilinger, p. 290, Figure 2.

Experiment and the foundations of quantum physics ... He has probably run the experiment, but that is just a guess. Entangled photons behave somewhat differently than other photons because they are in a different wave state.

Dr Chinese, I have to give you credit, when you make me look closer at something I at least find some deeper information and potential meanings, and learn more.
I doubt Zeilinger has tried the experiment he imagines in Part III of his foundations paper you linked us too.
In fact I rather regard him like Einstein considered some of his Professors, inconsistent and not in touch with the information he is presenting, at least in this section. But he does reference a source experiment later in Part III, from a 1998 Ph.D thesis by B Dopfer (University of Innsbruck), from which he claims:

We note that the distribution of photons behind the double slit without registration of the other photon is
just an incoherent sum of probabilities having passed
through either slit and, as shown in the experiment, no
interference pattern arises if one does not look at the other photon.

The key is no correlation or knowledge of the other entangled photon is considered at all.
IMO this gives a condition that not even QM can explain.
It means that an experimenter given a beam of light without knowing its source, could determine whether or not it was entangled based solely on the beam and no other information. If we send him light from a Laser he can generate double slit patterns. But if we send him just one beam of entangled photons with no access to the entangled beam we are to believe he would discover the beam is entangled as attempts to generate that pattern will fail.
Balderdash! There is no such wave state of an entangled beam that can do that.
THE PROBLEM IS the B Dopfer thesis does NOT make that claim!

A hard document to find, in its original language it can be found at;http://www.quantum.univie.ac.at/publications/thesis" . Figure 4.6 (Abbildung 4.6) is clear enough in any language that the lack of a pattern with the double slit is shown WITH a registration, and correlation of detections in the other beam. That is you must look at the other photon to get a no pattern view. IMO a rather embarrassing detail for the Zeilinger paper, and that section of his paper is clearly flawed.

I really would like to be able to read the Dopfer paper; it has data and ideas in the figures hard to explain. (I still need to understand just what a Heisenberg Lens does).

If anyone comes across a English translation of the 146 page Dopfer paper I'd like to read it.

Also he figure on Page 12 of the thesis also confirmed my expectation that the shape of a Type I SPDC is significantly different than a Type II.
I can see why polarization entanglement tests use Type II.
Good cartoon at opening of Dopfer paper.

 

[RandallB]

Although I don’t like the comments in part III of the A. Zeilinger article, I’ve got to give the Professor a great deal of credit for maintaining the Dopfer thesis paper on his University Web Site. It has a great deal of detail explaining exactly how and what was seen in an inspired experiment.
Even thou it requires using a tedious bit by bit translation by pasting into google translator, with some words not translating from the German, I’ve learned quite a bit.

I think I finally understand there is no such thing as a Heisenberg lens or detector except when a normal lens and detector are configured together creating a ‘Heisenberg microscope’ type measurement.
Also I think I mentioned how the figure on Page 12 of the thesis (page 18 of the PDF file) is the first time I’ve understood what a Type I Parametric Down Conversion of light looks like.

But most exciting is how mysterious the detail of photon positions are when measured between progressive screen distances in leg 1 correlated with double slit and single slit results in leg 2. The experiment is a brilliant combination of the two slit and entanglement paradoxes. From what I’ve been able to draw out of the data, it is almost mystic how the photons position themselves between the one and two focal lengths of the “H” lens.

I am not able to see how a theory like BM, or others like it, can explain the observations.
IMO the original QM does a better job.
But I must admit I’m not good enough at the QM formalisms or math to confirm that as a fair evaluation.
Even though it is hard to follow the German, I think you will the Dopfer thesis paper worth looking at.
RB

 

[JesseM]

IMO this gives a condition that not even QM can explain.
It means that an experimenter given a beam of light without knowing its source, could determine whether or not it was entangled based solely on the beam and no other information. If we send him light from a Laser he can generate double slit patterns. But if we send him just one beam of entangled photons with no access to the entangled beam we are to believe he would discover the beam is entangled as attempts to generate that pattern will fail.
Balderdash! There is no such wave state of an entangled beam that can do that.
THE PROBLEM IS the B Dopfer thesis does NOT make that claim!

Why do you think there is a problem with entangled photons behaving differently than other photons? This is exactly what happens in the delayed choice quantum eraser--the "signal" photons can come from one of two origins, just like the slits in the double slit experiment, and the total pattern of signal photons never shows any interference, although if the which-path information of the entangled "idler" photons is erased, then you see interference when you do a coincidence count between idlers that were detected at a particular detector and the signal photons.

 

[RandallB]

Why do you think there is a problem with entangled photons behaving differently than other photons?

Because as far as I know the ONLY time entangled photons ever seem to act differently than others is when they are measured with “coincidence counting” or correlations. With two entangled beams (signal and idler beams) IMO if you take just one beam (signal or idler) and ignore the other (direct it to space or a black body) and only look at the one beam by itself; is see no reason to expect any measurable character in or from the one beam to distinguish as entangled or different than a solo beam coming directly from a laser through a polarization filter.

The A. Zeilinger article claims to see no interference pattern without registration/ correlation of the other photons.
But the paper he cites shows no such thing.
The Dopfer thesis is not that hard to follow even in German to see that the results found in the actual experiment shows the pattern at the ‘Doppelspalt’ detector only disappears when measured in correlation with the other beam measured at the 2f distance.
No claim is made that correlation is not required to get the pattern to disappear.

Proving the Zeilinger claim would be easy, just a PDC sending one side to a Two Slit to produce a pattern or not.
No counting equipment required.
I’d bet anything that the pattern shows.

 

[JesseM]

Because as far as I know the ONLY time entangled photons ever seem to act differently than others is when they are measured with “coincidence counting” or correlations.

"As far as you know" perhaps, but do you have any reason to think this should be a universal rule? Again, if you look carefully at the DCQE experiment you will see that the signal photons do behave differently from non-entangled photons, in the sense that their total pattern never displays interference. Coincidence counting signal photons with idler photons found at a particular detector can show an interference pattern if the idler's which-path information is erased, but the sum of the coincidence counts for the idlers at different detectors gives a non-interference pattern.

With two entangled beams (signal and idler beams) IMO if you take just one beam (signal or idler) and ignore the other (direct it to space or a black body) and only look at the one beam by itself; is see no reason to expect any measurable character in or from the one beam to distinguish as entangled or different than a solo beam coming directly from a laser through a polarization filter.

Again, just look at the details of the DCQE experiment and you can see this expectation is wrong. Would you claim that the total pattern of signal photons in the DCQE experiment would show interference, or that non-entangled photons emitted from one of two locations in such a way that it was unknown which location a given photon came from would fail to create an interference pattern?

Proving the Zeilinger claim would be easy, just a PDC sending one side to a Two Slit to produce a pattern or not.
No counting equipment required.
I’d bet anything that the pattern shows.

I would expect that even without running the experiment, it would be simple enough to calculate what orthodox QM predicts should happen in this situation.

 

[vanesch]

"As far as you know" perhaps, but do you have any reason to think this should be a universal rule? Again, if you look carefully at the DCQE experiment you will see that the signal photons do behave differently from non-entangled photons, in the sense that their total pattern never displays interference.

Well, if you only look at ONE beam, you cannot distinguish "entangled" photons from a statistical mixture of "non-entangled" photons. That's easy enough to show: all observables acting ONLY upon one beam have all their expectation values determined by the reduced density matrix where the second beam has been traced out.
Now, this reduced density matrix is identical with, well, a density matrix of the same form. So this means that there's no means to distinguish, with any kind of measurement that acts ONLY upon the first beam, between both identical density matrices.

Of course, you can distinguish them from the moment that you also do measurements on the second beam (in other words, when you look for correlations between both beams), because then you look at observables acting upon both beams, and their expectation values are NOT determined by the reduced density matrix. But as long as you confine yourself to one single beam, it will be equivalent to some statistical mixture of "non-entangled" photons with an identical density matrix as the reduced density matrix, for all possible and imaginable measurements.

 

[JesseM]

Well, if you only look at ONE beam, you cannot distinguish "entangled" photons from a statistical mixture of "non-entangled" photons. That's easy enough to show: all observables acting ONLY upon one beam have all their expectation values determined by the reduced density matrix where the second beam has been traced out.
Now, this reduced density matrix is identical with, well, a density matrix of the same form. So this means that there's no means to distinguish, with any kind of measurement that acts ONLY upon the first beam, between both identical density matrices.

Of course, you can distinguish them from the moment that you also do measurements on the second beam (in other words, when you look for correlations between both beams), because then you look at observables acting upon both beams, and their expectation values are NOT determined by the reduced density matrix. But as long as you confine yourself to one single beam, it will be equivalent to some statistical mixture of "non-entangled" photons with an identical density matrix as the reduced density matrix, for all possible and imaginable measurements.

But how does this work in terms of the DCQE experiment? See http://arxiv.org/abs/quant-ph/9903047 for the setup...looking at figure 1 and the associated graphs, I assume that the total pattern of signal photons at D0 would never show interference, since if you remove the beam-splitters BSA and BSB the total pattern of signal photons at D0 should look like the sum of the D3-D0 coincidence count and the D4-D0 coincidence count, neither of which show interference themselves (the D3-D0 coincidence count is shown in Fig. 5). Replacing the beam-splitters cannot change the pattern of signal photons at D0, since what you do with the idler should not have an observable effect on the signal photons before you do a coincidence count (if it did, that would imply the possibility of FTL communication). So in terms of what you're saying above, perhaps the total pattern of signal photons at D0 would be equivalent to a mixed state of non-entangled photons emitted from either location A or location B in Fig. 1? (perhaps you were referring specifically to a mixed state when you said 'you cannot distinguish "entangled" photons from a statistical mixture of "non-entangled" photons.') I don't see how it could be equivalent to a pure state where non-entangled photons are emitted from either A or B without leaving any evidence of which location they came from, since this should be equivalent to the ordinary double-slit experiment where you would see an interference pattern at D0.

 

[vanesch]

perhaps you were referring specifically to a mixed state when you said 'you cannot distinguish "entangled" photons from a statistical mixture of "non-entangled" photons.') .

Yes, that is exactly what I'm saying.
The reduced density matrix is not the density matrix of a pure state (rho = rho^2).

In fact, there is an equivalence between "statistical mixtures" and "entangled pure states".