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Interference seen in a member of an entangled pair

  1. Dec 27, 2008 #1
    Say we have two electrons in a spin entangled state about the z-axis |01> + |10>. One electron travels off to our left, the other to our right. The right electron passes through an inhomogeneous magnetic field with gradient solely in the z direction (Stern-Gerlach type), and subsequently passes through an appropriately placed plate with 2 slits, and then to a screen where its position can be measured. Basically a Stern-Gerlach magnet followed by an appropriately placed double slit experiment.

    If we do NOT measure the spin of either electron then isn't it true that, after repeating this experiment several times, the right electron will show an interference pattern on the screen? If we DO measure the spin of the left electron then isn't it true that we will not see the interference pattern (since we know the spin and therefore deflection and which-slit info for the right electron)?

    Evidentially there is something wrong with the argument above because, if it were true, then it would be a conceptually trivial way to communicate information faster than c -- someone at a (theoretically) arbitrary distance away can decide to measure the spin of the left electron or not, and another person at the screen after the double slit can see what the other person did (essentially a binary signal).

    Question:
    What is wrong with the conclusions I'm making about the above experiment?

    PS:
    I asked this question on this or another form a long time ago, but I'm asking again because the only answers I received were things like "it's impossible to transfer info faster than c." What I am wanting to know is exactly where/why the above experiment breaks down.
     
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  3. Dec 27, 2008 #2
    As I remember from reading Anton Zeilingers books a while ago, performing an experiment like this requires an experimental setup in which interference will become visible only by analysis of the data. For example, one needs a relatively large source of light, which causes any interference patterns to overlap such that the data at first appears random, and in fact it is random. The interference is then only discoverable in the correlation to the other particle. Whether such a correlation will exist depends on the measurements being performed, but in either case any particle which is allowed to show interference will only display random behavior.

    In order to allow both particles of an entangled pair to show interference, they need to be created in such a way that both particles will show random behavior when examined individually. (At least that's how I understood it).
     
  4. Dec 27, 2008 #3
    Yes, its a common misconception. I see it in some results of the Quantum Erasure experiment too. Implying FTL as you suggest.
    My take is this: When the spin of one of the entangled particles is measured we can say that the other had the opposite spin at that exact time - if we had been clever enough to measure it (at that exact time, remember). But subsequently, its back to a probabilty of either spin because its in superposition still i.e. the wave function has both spins. Its not as if measurement of one 'particle' converts the other particle to one of the opposite spin. It would indeed be useful if that were the case (we could then have FTL).

    We would only be certain that the other particle had the opposite spin at one instant only and not know after that time exactly what the spin were - it would be a probability again as given by the amplitude function etc.
     
    Last edited: Dec 27, 2008
  5. Dec 27, 2008 #4

    Doc Al

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    Imagine that all of the left members of the entangled pairs go to Lab A and the right ones go to Lab B. Nothing done in Lab A can have any effect on the results of measurements made in Lab B (assuming the Labs do not communicate). Lab B experimenters would have no way of knowing whether Lab A even made any measurements, much less what the results were--for all they know Lab A could have been destroyed before any measurements could be made.

    Of course, if you use the results of measurements made in Lab A to filter out a subset of Lab B results, interesting effects can be achieved. But that requires ordinary non-FTL communication between the Labs and cannot be used to send FTL signals.
     
  6. Dec 27, 2008 #5
    LaserMind: I believe that, once a particle (or its entangled counterpart) is measured in a particular spin state, it remains in that state until something is done to its spin, like a measurement of spin about x, .... For example, Feynman lectures says that if you pass electrons through a z-oriented Stern-Gerlach (SG) and send the spin up electrons through a second z-oriented SG then all the electrons passing through the second SG will be measured spin up (they retained their spin up property). However, if you pass the spin up electrons through a x-oriented SG before passing them through the second z-oriented SG, then you will see only half of the original spin up electrons measured spin up in the second z-oriented SG.

    Doc Al: So you are saying that, whether or not we measure the spin of the particles, it has no effect on the measurements of the right particle hitting the screen. What WILL we see when the right particles hit the screen? I guess it will not be an interference pattern because it seems like we will end up with contradictions if we think that through, for example:
    Every 10 seconds we send the entangled pairs out to labs A and B.
    Lab A measures and records the Z component of the spin of each (left) electron:
    Electron@T=0: up
    Electron@T=10: down
    ...
    Electron@T=100: up
    Lab B measures and records the location at which each (right) electron hits the screen:
    Electron@T=0: position21
    Electron@T=10: position15
    ...
    Electron@T=100: position34
    Afterwards, Alice in lab A calls Bob in lab B and tells him the spin of each electron. Now Bob saw an interference pattern, but he also knows which slit each electron passed through, a contradiction, right?

    Main question: What will Bob see and why? If the answer is that Bob sees no interference pattern, and that the electrons go straight through just as if Bob observed the which-way info, then my next question is how those results remain the same when Alice closes lab A and no longer measures the spin (what causes the interference pattern to disappear when we haven't measured the which-way info)?

    Thanks!
     
    Last edited: Dec 27, 2008
  7. Dec 28, 2008 #6

    DrChinese

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    Well, we know there is actually no contradiction and no FTL signaling possible. So let's take a close look.

    1. The tacit assumptions present in your example are:

    a) Alice and Bob would exhibit "perfectly" symmetric correlations of their path through the slits (i.e. which slit), assuming that you perform exactly the same experiment for both.

    b) Entangled particles individually exhibit self-interference when going through a double slit, no differently than an un-entangled particle.

    2. So what about these assumptions? a) is true but b) is not. When you check ANY observable on Alice you will ALWAYS see a correlated value for Bob after an identical test. The test on Bob is essentially redundant (since no new information was obtained). This was the starting point for the EPR argument.

    But Alice and Bob do NOT exhibit self-interference as do particles that are not entangled! As a reference on this point, see Zeilinger, p.290, figure 2.

    3. Entangled particles can be made to self-interfere in some cases. However, in those cases the entanglement will have already been terminated and now assumption a) above is no longer valid.
     
  8. Dec 28, 2008 #7
    I'm not sure which cases you are referring to, however I think it is worth mentioning that in the "double-double-slit" experiment (which might be just a thought experiment by A.Zeilinger), both particles can (or are expected to) show an entangled interference pattern, however this pattern is only visible in hindsight, using data exchanged in a classical way, through analysis of the entanglement-based time correlations and a specific experimental setup (which might only analyze one of the patterns at a time, so to speak). Unfortunately quite complicated, this is described in at least one of A.Zeilingers books.
     
  9. Dec 28, 2008 #8
    Thanks for the great info. I'm checking out the Zeilinger paper.
     
  10. Dec 29, 2008 #9
    Re Zeilinger Paper, FIG 2. http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf

    Referring to interference patterns for entangled particles, one of which passes through a double slit.
    If one entangled particle travels in the opposite direction then there is no interference pattern given by the
    particle that went through the double slit because the superpositon would cancel intensities out exactly - except
    at the particle positions, and not primarily because 'there is a possibilty of knowing which path'. Using wave packet analysis which path (of a particle!!) plays no role - there is no particle its a wave packet as in CI. The 'particle' is a position state observable. Similarly for 'waves', thats another state observable. Cannot we finally get away from the old wave particle duality issue?
    I refer to: http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf FIG 2.
    There were two wave packets (as per CI) that went through each slit, and the resulting interference makes
    it look like only particles went through one or the other slit.
    If wave packets are analysed instead of trying to think about particles or waves then statements such as 'the possibilty of
    knowing which path' appear unscientific to me, - the wave packets go down all possible paths allowed by experimental set ups.
    The wave packets of entangled particles then have more components to consider which give rise to interference patterns or lack of.
     
  11. Dec 29, 2008 #10

    DrChinese

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    Yes, and that is why there are no FTL signaling possibilities (the OP raised that idea). But looking on one side by itself, there is no traditional interference pattern.
     
  12. Dec 29, 2008 #11

    DrChinese

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    Welcome to PhysicsForums!

    Not sure I follow your comment exactly. You can easily tell which slit the entangled photon traverses since there is no interference pattern. Just place a detector behind each slit. Learning that info for Alice will allow you to predict the result for Bob. But that does not violate CI, nor the HUP.
     
  13. Dec 29, 2008 #12
    Yes, no traditional, immediately visible pattern.

    The known effects of entanglement are always a symmetric relation of otherwise random events. "Random" means subject to the Heisenberg uncertainty principle. Their uncertainty is coupled. If the experiment doesn't "allow" the particles to be uncertain in some property, then there can't be any entanglement in that property, in so far as is known (or as I know).

    ------ EDIT: --------

    For such experiments where the uncertainty (via interference) itself becomes the observed property, the seemingly unavoidable obstacle is that in order to entangle two particles in way that they can show interference for the entangled property, one needs a different source than one needs to create just one particle with uncertainty (showing interference).

    As far as I have understood, this is again due to the HUP, within the source. In order to be entangled in such way that measurement on one particle would influence the interference pattern of the other particle, there needs to be an additional coupled uncertainty regarding, for example in a photon source, the location from where the particles originate. This uncertainty in the source location will cause the interference patterns to overlap such that they appear only as a random patterns (until they are analyzed via time coincidence using classically transmitted data from the other particle's measurements).
     
    Last edited: Dec 29, 2008
  14. Dec 31, 2008 #13
    I read the Zeilinger paper discussed (and linked to) above, which says that that a member of an entangled pair will only show self-interference if the which-way info for the entangled partner is destroyed. So what I was saying in the original post would NOT work.

    Zeilinger (pages 2-3) discusses an experiment by Dopfer in which the measurement of the which-way info of the entangled partner is turned on and off by moving the detector D1 for photon 1. So the interference pattern of the other photon (photon 2) is turned on/off be moving the detector D1. So I have to ask, why can't we use that for FTL communication? Someone can move D1, while someone else (arbitrarily far away) gets photon 2 and runs it through the double slit experiment to look for an interference pattern. What's wrong with this approach? I know you need N copies of this experiment run in parallel to really determine the existence of the interference pattern, but that's simple enough right?
     
  15. Dec 31, 2008 #14
    That is exactly the question I tried to answer above, especially in the "EDIT:" section. I' look forward to see an answer from someone more qualified (than me).
     
  16. Dec 31, 2008 #15

    Cthugha

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    See page 290 of the Zeilinger paper:

    The interference pattern in one leg is still conditioned on the registration of the entangled partner in the other leg. So the interference pattern will only show up in coincidence counting, which means that you will still have to get the information from one detector to the other in a traditional communication way. Therefore this setup does not allow FTL communication.
     
  17. Dec 31, 2008 #16
    I don't know what is meant by registration, but don't we know that roughly X percent of the photons will be registered when D1 is at the focal plane, and roughly Y percent will be registered when D1 is at the imaging plane? If so, can't we differentiate the patterns behind the double slit when:

    Case 1 (D1 at focal plane; trying to destroy the which way info):
    100-X percent of the photon's are not registered and effectively follow "patternA" behind the double slit
    X percent are registered and they follow "patternB" (interference pattern)
    NetPattern1 = (100-X)*patternA/100 + X*patternB/100

    Case 2 (D1 at imaging plane; NOT trying to destroy the which way info):
    100-Y percent are not registered and follow "patternA"
    Y percent are regestered and follow "patternC"
    NetPattern2 = (100-Y)*patternA/100 + Y*patternC/100

    Can't someone distinguish between NetPattern1 and NetPattern2? With arbitrarily high confidence by increasing N (=the number of experiments performed in parallel)?
     
  18. Dec 31, 2008 #17

    DrChinese

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    Following up on what Cthugha said and why you can't get FTL communication:

    There ARE some situations in which certain special kinds of interference patterns appear for entangled particles. These are NOT traditional double slit patterns similar to unentangled photons. That is what the Zeilinger reference is saying regarding Figure 2, which is showing the traditional double slit format.

    Unfortunately, most of the papers on this type of experiment are a bit complex, and they do not usually explain explicitly that the interference pattern is not the traditional double slit type on one side. In the special cases in which interference patterns can appear (such as Zeilinger's Figure 3), there are two critical factors:

    a) Coincidence counting is required involving measurements at both Alice and Bob. Obviously, you cannot get FTL communication if you need to first correlate results at Alice and Bob.

    b) The raw pattern that Bob sees is not conditioned on anything Alice does (such as moving Alice's D1 from one focal point to another). The image Bob sees stays the same! Now why is that, since clearly the coincidental counts drop to nearly zero in some of Bob's areas when Alice positions D1 at a precise point?

    Registering a photon at the focal point of a lens at Alice occurs randomly, and this occurs only a small fraction of the overall counts. You may find this easier to see if you look at the actual Dopfer data (see pages 56-58, in German). Looking at the detail (not given in the Zeilinger reference), I would estimate that only 80 in 300 photons registers this way. The other 220 go towards making up the overall image that looks like a traditional Bell curve. So when you look at the difference between one and the other of the positions Alice chose, there is little difference to see in the raw data Bob sees. By my very rough calculations, it would be right on the threshold of system noise and random variation. So nothing useful for Bob to see by way of a signal.

    If Dopfer had seen a change in the pattern at D2 after changing the D1 position, I think she would have been jumping for joy on the way to the patent office. After all, she had the raw data and this experiment is now 10 years old. Nonetheless, John Cramer has proposed that there should be a small differential that might be within the realm of visibility, stating:

    "In the Dopfer Experiment, the pattern in the lower detector was selected by requiring events in which detected photon were in good time-coincidence in both detectors. Therefore, it is possible (barely) that with no coincidences, the same raw pattern would appear in the lower detector, independent of the position of the upper detector, with the coincidences from the upper arm selecting from this raw pattern a diffraction pattern in Case 1 and an interference pattern in Case 2.

    However, this scenario seems unlikely. Around 85% of the photons in the lower detector should be in coincidence with photons in the upper detector regardless of position. Therefore, while the coincidence requirement should remove the 15% of noise, it should in itself do little else. In particular, it should not be able to thin out the raw pattern enough to produce the minima of the interference pattern.

    Unfortunately, the Dopfer thesis does not discuss what was observed in the lower detector with the coincidence requirement removed. For this reason, a crucial test of quantum phenomena would be to re-create the Dopfer Experiment and observe the role of the coincidence requirement on what is observed in the lower arm detector. Several research groups are considering doing this, but there are no results yet."
     
    Last edited: Dec 31, 2008
  19. Dec 31, 2008 #18
    Preliminary answer from a layman: Netpattern1 (interference) consists (except for some noise) of an superposition of multiple interference patterns. Without patternB, the remaining patternA does not have a completely random distribution anymore.

    Netpattern2 does not contain the same patternA, and so you don't get a meaningful result by subtracting patternA from Netpattern2. In both cases, it would look like the result is something like patternB, but in the second case, performing this calculation would be meaningless.

    In other words, both Netpattern1 and Netpattern2 are random, but in case 1 it is possible to select an interference pattern (using classically obtained information from measurements of the other particle), where the remaining pattern is not random either, but their sum is random. The superposition of a set of interference patterns which add up to a random pattern. At least that is my understanding of the current theory (in A.Zeilinger's books), and if that understanding is correct, it would take an actual experiment to show if it were otherwise.
     
    Last edited: Dec 31, 2008
  20. Dec 31, 2008 #19

    DrChinese

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    What we are trying to guess is whether the fringe spots with no intensity (when registered) might be detectable in a very tightly controlled setup in which there was a corresponding slight dip in the total at that fringe spot. That is what Cramer wondered, and msumm21 as well.

    Obviously, Dopfer noticed nothing. Obviously, there are no other prominent physicists who have published on this in the past ten years with a result supporting FTL communication.

    So here is a DrChinese going-out-on-a-limb prediction: The raw data will not show any difference at Bob (when Alice varies her detector positioning) regardless of experimental accuracy. This conclusion is based on a belief that there is no FTL signaling possible. Therefore, for this result to be correct, you merely conclude that the HUP is always at work - if in strange ways.

    What observation you choose at Bob must influence what happens at Alice as much as the reverse. So merely changing the Alice setup (between momentum and position observations) is only part of the equation. We still cannot exceed the limits of the HUP. Therefore something else must change. Presumably, there is an offsetting change in the distribution such that:

    Alice's detector at position 1:
    B1=
    Bob's detections at fringe area X, when Alice at fringe area Y +
    Bob's detections at fringe area X, when Alice not at fringe area Y

    Alice's detector at position 2:
    B2=
    Bob's detections at fringe area X, when Alice at fringe Y +
    Bob's detections at fringe area X, when Alice not at fringe Y

    B1 = B2, and this holds for any conditional of Alice, including any fringe area Y, even those where X=Y.

    We would expect this to be true, just like we expect polarization results to remain static for Bob regardless of changes in polarization observations at Alice. There is no difference.

    But the Dopfer results do show us something. Clearly, the observation at Alice can be chosen after the results are in at Bob - and the coincidence counts will still match predictions. We knew this already, from the earlier Aspect experiments for example. The difference in this case is: the influence of the change at Alice can be discerned (with coincidence counting); while in the Aspect experiment, it was not possible to see the effect of Alice's observation on Bob differently than Bob's observation on Alice (also with coincidence counting). So that is cool in Dopfer.

    Presumably, there would be a way to vary the observation at Bob so that either his result occurred either before or after the result at Alice. In that way, it might become clear that the the results are dependent on both entangled Alice and Bob equally, and that the sequence of measurement does not establish a preference in the results. :)
     
    Last edited: Dec 31, 2008
  21. Dec 31, 2008 #20
    Right, there are two questions:

    1. Is it possible to create an experiment where interference can be detected depending on an entangled particle, but without classically obtained data from that particle. (Apparently not.)

    2. If not, what is the explanation a) specifically within any (thought-) experiment, and b) generally, in theory.

    And, you could also base it on the belief that entanglement always only shows a relationship between two otherwise random events (which I understand, is suggested by the theory, their wavefunctions, etc.)

    As far as I understand, any (experimental, to this date) entanglement-specific results depend on both measurements, and therefore remain in uncertainty until the second one is made. And, they don't appear to depend on the sequence of measurement, each result, observed separately, is apparently random, and therefore (apparently) independent of what happens at the other particle. (This sentence was edited after posting).

    This implies, specifically in the case of observing interference, not only that data from the other particle is needed for detection of an effect, but also goes together with certain restrictions on what experimental setups are possible, in this case, that a particle source which is able to produce entangled particles with uncertain properties (which can interfere) will produce only a a set of superimposed interference patterns which in their sum appear random.

    Verifying that this is actually the case, in reality, requires verifying that particle sources (in this case a "UV pump", together with the crystal) indeed always have this limitation.

    On the other hand, if it were possible to build a particle source that doesn't have this limitation, then that would be a new discovery, also implicating a new or modified theory about entanglement and its basis. In my understanding.
     
    Last edited: Dec 31, 2008
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