A very simple question re: entangled photons

[craigmcewan]

Hi

I've been struggling to understand entanglement for some time now, and find that most explanations assume some basic knowledge that I don't have. Please could somebody help clear up a very basic query for me?

If two photons are entangled, and we have no knowledge of their state of polarisation:
If one photon is tested for horizontal polarisation, and passes, what is the probability that the other will pass a test for vertical polarisation?

I believe that I've read that the probability is 100%. Is this correct?

And if so, is it actually, experimentally 100% every time? One would expect experimental error to to produce a few failures, even if the theory says it's 100%!

I'd love to find a paper that describes this experiment clearly, in layman's terms. If anyone can direct me to such a paper, I would be very grateful!

Thanks in advance

Craig

 

[DrChinese]

Hi

I've been struggling to understand entanglement for some time now, and find that most explanations assume some basic knowledge that I don't have. Please could somebody help clear up a very basic query for me?

If two photons are entangled, and we have no knowledge of their state of polarisation:
If one photon is tested for horizontal polarisation, and passes, what is the probability that the other will pass a test for vertical polarisation?

I believe that I've read that the probability is 100%. Is this correct?

And if so, is it actually, experimentally 100% every time? One would expect experimental error to to produce a few failures, even if the theory says it's 100%!

I'd love to find a paper that describes this experiment clearly, in layman's terms. If anyone can direct me to such a paper, I would be very grateful!

Thanks in advance

Craig

Welcome to PhysicsForums!

A good paper is: Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory

Don't be surprised if it takes a few reads, and you end up looking back and forth at other articles to get the idea. Now, to answer your questions:

You are correct that if one of the pair is found to H, the other will certainly be V. This is usually what is called Type II PDC. In Type I PDC, if one is H then the other is also H (this is the case in the cited paper). But the correlations work essentially the same otherwise.

Is there experimental error? Yes, of course, you will be able to see that from the graph and the data. It is not 100% as both photons are not always detected. Sometimes one is detected on one side and there is no match (either H or V) on the other.

A couple of points:

They sometimes use Signal and Idler to refer to Alice and Bob or A and B. So don't let that confuse you.

In this experiment, there is a polarizer in place and the only photons that are detected are ones that make it through. In many experiments, a polarizing beam splitter is used instead, so both H and V photons are counted on both sides. This allows you to better see that the polarizer itself is not affecting the results so much.

I hope this helps, I have additional references on my Bell web page:

http://www.drchinese.com/Bells_Theorem.htm

 

[javierR]

Yes, if the photons are correlated with orthogonal polarization, a measurement of one's polarization must be orthogonal to the other's every time.
Maybe the page below helps, which is a student's overview of an experimental paper on photon entanglement. As for "interpretational issues", take what they say with a grain of salt. Interpretation is a debated subject; one of *my* preferred treatments is that of the "consistent histories" approach. Roland Omnes wrote several books on this, one or two of which are less technically demanding.
Student's write-up:
http://grad.physics.sunysb.edu/~amarch/
The original paper can be found at:
http://grad.physics.sunysb.edu/~amarch/Walborn.pdf
A brief description of "consistent histories" framework with seminar notes:
http://quantum.phys.cmu.edu/CHS/histories.html

 

[DrChinese]

Yes, if the photons are correlated with orthogonal polarization, a measurement of one's polarization must be orthogonal to the other's every time.
Maybe the page below helps, which is a student's overview of an experimental paper on photon entanglement. As for "interpretational issues", take what they say with a grain of salt. Interpretation is a debated subject; one of *my* preferred treatments is that of the "consistent histories" approach. Roland Omnes wrote several books on this, one or two of which are less technically demanding.
Student's write-up:
http://grad.physics.sunysb.edu/~amarch/
The original paper can be found at:
http://grad.physics.sunysb.edu/~amarch/Walborn.pdf

Yikes, are you sure about these? I consider this one of the more advanced experiments that should come well after normal entanglement. This provokes a lot of questions that even experts have a hard time with, in my experience.

 

[craigmcewan]

Thanks Dr Chinese

The paper you linked to does seem to be what I'm looking for... though I'm finding parts of it hard to understand, I'm going to persevere as you recommend.

Incidentally, it was reading your explanation of Bell's inequalities that led me to post my question. Your explanation is very clear, and certainly the best summary of the subject that I have come across so far.

Thanks for your time, it's much appreciated

Craig

 

[craigmcewan]

Thanks Javier for that link

The paper refers to the orthogonal polarisation of entangled photons as a known fact, rather than actually demonstrating it... however, what an elegant experiment! It is this kind of bizarre behaviour that has sparked my interest in the field of quantum entanglement.

The student's write up is great, much easier to understand for a beginner like me, but I do like to have the original paper, which you also linked to.

Thanks for taking the time to pass on these links, much appeciated

Craig

 

[zonde]

And if so, is it actually, experimentally 100% every time? One would expect experimental error to to produce a few failures, even if the theory says it's 100%!

There are of course experimental errors and they are tested using negative correlation. That's the orientation of polarizers when no coincidences theoretically should be detected.

I'd love to find a paper that describes this experiment clearly, in layman's terms. If anyone can direct me to such a paper, I would be very grateful!

I can recommend this paper if you like visualizations:
http://arxiv.org/abs/quant-ph/9611037v3"

 

[DrChinese]

I can recommend this paper if you like visualizations:
http://arxiv.org/abs/quant-ph/9611037v3"

zonde, why are you giving this as a visualization when it is wrong? That does not seem helpful. If you have a reference that is reputable for the subject, that is fine, but this is no good - especially for those wishing to learn about Bell. If you want to solve the visualization problem, you must look to interpretations.

 

[zonde]

zonde, why are you giving this as a visualization when it is wrong? That does not seem helpful. If you have a reference that is reputable for the subject, that is fine, but this is no good - especially for those wishing to learn about Bell. If you want to solve the visualization problem, you must look to interpretations.

This discussion of the same subject in two thread is a bit weird.
But well I have not seen any visualization as good and as simple as her visualization. It just makes things look simple. I do not understand why things should look complicated.

 

[craigmcewan]

Reply to Dr Chinese

Hi Dr Chinese

Ok, I've spent some time with the paper you recommended
(http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf).

I admit that the maths is beyond me, but if I understand the experimental set-up correctly, a count is only made if both entangled photons in a pair pass through their respective polarisers, and hit their respective detectors at a close enough time to trigger the coincidence counter.

The experimenters found while setting up the equipment (at the end of Section IV. Setup) that with the irises fully open, and both polarisers set to vertical, over 300 counts per second were seen.

According to theory, there should be no photon pairs in which only one photon passes through its polariser (this is the part of theory that my original post asked about). However, if only one photon passed, the coincidence counter would not fire, and no measurement would be made. These pairs would not contribute to the results at all.

Therefore, as I understand it, the purpose of this experiment is not to demonstrate the effect that I was asking about, which was:

"If two photons are entangled, and we have no knowledge of their state of polarisation:
If one photon is tested for horizontal polarisation, and passes, what is the probability that the other will pass a test for vertical polarisation?
I believe that I've read that the probability is 100%. Is this correct?"
(of course in this experiment, both would be tested for vertical polarisation because it uses Type I PDC as you explained).

Sorry if I seem to be asking for a re-invention of the wheel, as I realize that everyone accepts this result- but it seems very important to me, and in a way is just as amazing as the more flashy results that later experiments have found (like JavierR's fantastic quantum eraser link).
For this reason I really want to find a paper that describes an experiment in which this is demonstrated. I don't think I can move on to the exotic implications of entanglement without properly grasping this point. So: any more ideas? Anyone?

Thanks again for taking the time to read and reply my post, it is very generous of you all

Craig

 

[DrChinese]

I admit that the maths is beyond me, but if I understand the experimental set-up correctly, a count is only made if both entangled photons in a pair pass through their respective polarisers, and hit their respective detectors at a close enough time to trigger the coincidence counter.

The experimenters found while setting up the equipment (at the end of Section IV. Setup) that with the irises fully open, and both polarisers set to vertical, over 300 counts per second were seen.

According to theory, there should be no photon pairs in which only one photon passes through its polariser (this is the part of theory that my original post asked about). However, if only one photon passed, the coincidence counter would not fire, and no measurement would be made. These pairs would not contribute to the results at all.

You may not fully follow the experimental setup and/or the theory behind it, but I definitely feel you have gained from looking at this. You are correct as to how the basic coincidence count is performed. It is not correct that theory says there should be no situations in which only 1 photon passes the polarizers. The coincidence count is from 2 hits. 1 hit at A, 1 hit at B, or 0 hits is not a coincidence in this case. That occurs at some angles more than others.

Generally, the QM predicted theoretical rate for coincidences is cos^2(theta), where theta is the angle in between the settings. For example, if the settings are 0 degrees and 90 degrees then theta=90 (this is where coincidences are at a minimum). The rate for non-coincidences is simply 1-(cos^2(theta)), which is the same as sin^2(theta).

In other words, there is a maximum setting for getting coincidences. When set for that, coincidences max out around 300. When set at the angle that a minimum should occur at, there are about 20. This is within experimental bounds, the theoretical might be considered as 0. The graph (3.a., alpha=0 degrees) shows what happens when you rotate through 180 degrees.

So to answer your question: at A=0 and B=0, there is a maximum of coincidences. That is equivalent to 100% relative to experimental accuracy. You cannot see the "missed" photons in this particular setup. As mentioned previously, you need a setup with polarizing beam splitters (and 2 detectors per side, 4 total) if you want to detect both H and V photons on a side. But the results don't actually change at all, it just allows you to see what you are "missing".

So if you are trying to prove that the probability of an H at Alice being also an H at Bob when theta=0 is actually 100%, you need to look at the missing photons and will need the PBS. (Or alternately, you will need to know what the coincidence rate is IF you take both polarizers out in the referenced experiment. You would expect that to be about 600. I don't see this in the paper. In this experiment, a reasonable person would deduce the correct behavior you are looking for because of the existence of the cos^2 relationship and the violation of the Bell Inequality.)

 

[zonde]

According to theory, there should be no photon pairs in which only one photon passes through its polariser (this is the part of theory that my original post asked about). However, if only one photon passed, the coincidence counter would not fire, and no measurement would be made. These pairs would not contribute to the results at all.

If I understand correctly what you are asking for then maybe this experiment will look interesting for you:
http://arxiv.org/abs/quant-ph/9810080v1"
In this experiment all clicks in detectors are recorded with timestamps and coincidences are found out later using recorded data.

 

[DrChinese]

If I understand correctly what you are asking for then maybe this experiment will look interesting for you:
http://arxiv.org/abs/quant-ph/9810080v1"
In this experiment all clicks in detectors are recorded with timestamps and coincidences are found out later using recorded data.

Good reference!

 

[Peter Morgan]

Hi craigmcewan,
Let me tackle your question from a slightly different perspective. Suppose we set up an experiment that has four "detectors" that make thermodynamic transitions from their ready state to an excited state when we shine (faint) light on them. Suppose that we record the times at which transitions from the ready to the excited state happens in each of the four detectors. If one, two, three, or four transitions happen at the same time, then -- in quantum theory, for apparatus that we believe is capable of responding to single photons -- we say that one, two, three, or four photons, respectively, caused the transitions we see. (Zonde's reference is a fairly classic use of four detectors. The explicit recording and reporting of the times at which every detector transition event happens is, in my opinion, a paradigm for quantum optics. I second DrC's further recommendation).

The rates at which we see such isolated or simultaneous events in the four detectors depends on what kind of light we shine on the detectors. If we shine light on only one of the detectors, we will only observe single events in that one detector. If we shine light on all four detectors rather carelessly, we will observe single events in each of the detectors, but we will only occasionally observe simultaneous events in two or more detectors, which will be no more than the random coincidences we would expect of four independent classical time-series. The job of the experimenter is to produce bizarre statistics of simultaneous events, ideally that no-one has managed to produce before, by constructing bizarre light sources, which cause, in particular, a lot more simultaneous events than are caused by just carelessly shining light on the four detectors.

It's a matter of fact that experimenters can produce statistics of simultaneous events that are bizarre enough that we can't construct classical particle models for them (except for de Broglie-Bohm or Nelson-type models that introduce nonlocal interactions that are not very natural for classical particles), but it's not that easy, so that an experimenter has to characterize their light sources by measurement (using the four detectors, for example), to find out what light source they are producing. One can buy off the shelf components, but that's just because someone else has done the characterization of the light source, so the experimenter can produce a still weirder and more interesting state without reinventing the wheel every time.

Note that there is a chicken and egg problem. We don't know what our light source does until we put it close to a few detectors and measure the response, including determining what simultaneous events occur, but we also don't know what our detectors response is until we characterize them with light sources that we have previously characterized. There are reasonable lab procedures for coping with this, but you have to ensure that the four detectors can reasonably be said to be measuring the Horizontally and Vertically polarized components of light for each of two wave numbers (as it typically would be in quantum optics). For careful experiments, one has to characterize as formally and precisely as possible how far the detectors fall short of the ideal measurement we would like them to perform.

 

[RUTA]

Therefore, as I understand it, the purpose of this experiment is not to demonstrate the effect that I was asking about, which was:

"If two photons are entangled, and we have no knowledge of their state of polarisation:
If one photon is tested for horizontal polarisation, and passes, what is the probability that the other will pass a test for vertical polarisation?
I believe that I've read that the probability is 100%. Is this correct?"

If you don't know their initial state, you can't say what will happen. You're describing the singlet state here: |+-> -|-+>. In that state, you will get coincidence counts when your polarizers are at 90 deg. If you rather have |++> + |-->, as in "Entangled photons, nonlocality, and Bell inequalities ..." cited above, you will get coicidence counts when your polarizers are set to the same angle. You have to know |psi> and making a particular |psi> is a big part of the experiment (read sections III - VI of the AJP paper and you'll appreciate how difficult it is).

 

[Peter Morgan]

Google finds the AmJPhys paper for which DrChinese cites the arXiv version, Am. J. Phys. 70 (2002) page 903. AmJPhys usefully lists papers that have cited this paper since then,
# Low-cost coincidence-counting electronics for undergraduate quantum optics
D. Branning et al., Am. J. Phys. 77, 667 (2009)

# Hidden variable theories and quantum nonlocality
A D Boozer, European Journal of Physics 30, 355 (2009)

# Interactive screen experiments with single photons
Patrick Bronner et al., European Journal of Physics 30, 345 (2009)

# Single-qubit tests of Bell-like inequalities
F. De Zela, Phys. Rev. A 76, 042119 (2007)

# Phase shifting of an interferometer using nonlocal quantum-state correlations
E. J. Galvez et al., Phys. Rev. A 75, 020302 (R) (2007)

# Quantum mysteries tested: An experiment implementing Hardy's test of local realism
J. A. Carlson et al., Am. J. Phys. 74, 180 (2006)

# Two particles in a double well: illustrating the connection between entanglement and the speed of quantum evolution
S Curilef et al., European Journal of Physics 27, 1193 (2006)

# Comparing quantum and classical correlations in a quantum eraser
A. Gogo et al., Phys. Rev. A 71, 052103 (2005)

# Interference with correlated photons: Five quantum mechanics experiments for undergraduates
E. J. Galvez et al., Am. J. Phys. 73, 127 (2005)

# Quantum entanglement, spin-1/2 and the SternGerlach experiment
G B Roston et al., European Journal of Physics 26, 657 (2005)

# Observing the quantum behavior of light in an undergraduate laboratory
J. J. Thorn et al., Am. J. Phys. 72, 1210 (2004)

# Entangled photon apparatus for the undergraduate laboratory
Dietrich Dehlinger et al., Am. J. Phys. 70, 898 (2002)

If you have access to a wealthy enough academic library, you can probably get these directly. Otherwise, you can try the authors' websites for the authors' offprint PDFs, google for the article titles, or search for the article titles on arXiv directly. Once you have a good article, it's always worth looking for anything that cites it.

 

[craigmcewan]

Thanks

Hi guys

Thanks for all the help- this suggestion from Zonde is exactly what I'm looking for. It's a very clear description of a rigourous experiment. Thanks Zonde

If I understand correctly what you are asking for then maybe this experiment will look interesting for you:
http://arxiv.org/abs/quant-ph/9810080v1"
In this experiment all clicks in detectors are recorded with timestamps and coincidences are found out later using recorded data.

Also big thanks to Peter Morgan; I do have access to a University library, so I should be able to get copies of many of the papers you suggested.

It's been very gratifying to get useful replies to my post from so many of you- I didn't think you physicists would be able to think down to my level!
No doubt I'll be posting again next time I need help; in the meantime I really appreciate the time you've all spent helping me out.
Thanks all!

 

[Haelfix]

Check out Susskinds lectures on entanglement as well for a video presentation. You can find them on youtube or the stanford site. 8 lectures of ~ 2hrs each.

The section on bells theorem is particularly lovely and intuitive.