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I What destroys interference: Possibility or actual measurment?

  1. Nov 28, 2016 #1
    Hi.

    If we place two perpendicularly oriented linear polarizers at a double slit, there will be no interference pattern. In the wave picture, this is trivial: Two waves with perpendicular polarization cannot interfere.

    In a quantum picture, I've often seen the interpretation that the sheer possibility of finding out which path a photon took (by measuring its polarization) destroys the interference, even if this measurement hasn't been performed.

    Now there's those infamous delayed choice quantum eraser experiments: Apparently one can measure the path information (thereby destroying interference) and erase it to restore the interference patter (using some rather shady post-processing). This appears to me as if the actual performance of a measurement of the path information destroys interference, and apparently it can be undone.

    So what exactly destroys interference: Is it the sheer possibility of measuring the path information or does it need an actual measurement?

    Is the "measurement and erasure" procedure in a quantum eraser experiment even a measurement in the orthodox (Kopenhagen) sense, i.e. is it a projection, or is it more of a unitary time evolution?
     
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  3. Nov 28, 2016 #2

    DrChinese

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    There must be the possibility of obtaining the information. In this sense, the measurement can be performed and then the information discarded - or not. There will be no interference.

    On the other hand: If the measurement is performed and then "erased" - by eliminating any and all traces of the results - then there is interference (i.e. it is as if the measurement never happened). Typically this involves restoring the quantum state prior to measurement.
     
  4. Nov 29, 2016 #3

    A. Neumaier

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    It is the presence of an interaction with the environment. This means that some information is passed to the environment, even when it is impossible to actually measure it.
    ''Erasure'' of true measurements is impossible; in the experiments that carries this name the measurement is not actually performed. Performed measurements must leave a macroscopic, on the microscopic time scale permanent record and are therefore always irreversible, by definition.
     
  5. Nov 29, 2016 #4

    vanhees71

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    The interference terms vanish, because the partial beams of particles running through the slits with perpendicularly oriented polarization filters is in the formalism due to the fact that the corresponding states are orthogonal to each other. Physically it describes a strict entanglement between which-way information and polarization of the particle that has run through the double-slit setup since the polarization filters impose the corresponding polarization state on each particle running through it. That means that by measuring the polarization of the particle you know through which slit it has come, and whether or not you measure it the which-way information is carried by the particles' polarization state. So there is no interference pattern, because you can distinguish through which slit each particle came with certainty.

    If you slight distort the polarization filters from not exactly being perpendicularly oriented, you get an interference pattern but also loose the certainty through which slit it has come. The more uncertain the which-way information gets (at the extreme you orient both polarizers exactly parallel, and then you cannot distinguish through which slit each particle came at all), and the interference pattern gets it's highest contrast.

    There's the fascinating possibility thanks to the possibility to create polarization-entangled photon pairs to "erase" which-way information after all measurements are done. You get then subensembles of the full ensemble of measured photons which show an interference pattern, while the total ensemble refers to one where you have which-way information (in principle), and thus there's no interference pattern. For details, see

    https://arxiv.org/abs/quant-ph/0106078
     
  6. Nov 29, 2016 #5

    DrChinese

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    As far as I know, you are right about experiments labeled as "erasure". However, there are others that have long been postulated - I can't say if they have actually been performed or not.

    J.H. Eberly, Bell inequalities and quantum mechanics (2001)
    http://www.pas.rochester.edu/~advlab/Eberly_Bell_Inequalities_AJP.pdf
    See Figure 1, itself taken from A.P. French and E.F. Taylor, An Introduction to Quantum Mechanics (1979).
    See also Figure 2.

    You can see that the idea is that a PBS measures the polarization of a photon. Then the PBS outputs are recombined by a second "reverse" PBS, before anything is recorded indicating which path the photon took. The original photon state, prior to entering the first PBS, is restored.

    So in fact it would be reversible measurement, if they are correct. I believe that an entangled photon, run through a suitable version of Figure 1, would in fact remain polarization entangled afterwards. Thoughts?
     
  7. Nov 29, 2016 #6

    A. Neumaier

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    In Figure 1, nothing is measured at all, and the author's don't claim that anything is measured.
     
  8. Nov 29, 2016 #7

    DrChinese

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    Sure something is measured by the first PBS: polarization. Of course it is the entire measurement context that matters. The second PBS reverses the initial measurement, so it is as if it never happened. Net: nothing is measured. My original statement on which you commented:

    "If the measurement is performed and then "erased" - by eliminating any and all traces of the results - then there is interference (i.e. it is as if the measurement never happened)." But something did happen at a quantum level, it just happens to net out in the example.

    It is obvious that the first PBS does in fact split the photon into 2 distinct paths. These components can be manipulated independently. You could rotate one or both of them, for example. You could alter their path lengths. And you can even recombine them into something close to their original. When you do the last operation, you have the potential to restore the original input entangled state. That entangled state could not be evidenced from either component alone, must first be recombined.

    So depending on your semantics: there is measurement, and then "erasure". Or you can say there was no measurement at all. I say the first is more descriptive.
     
  9. Nov 29, 2016 #8

    PeterDonis

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    One answer that seems to be increasingly popular with quantum physicists: decoherence.

    Another possible description would be to say there was measurement, but not decoherence. The lack of decoherence is what makes the erasure possible. But not all physicists would agree with this definition of "measurement", since one such definition is that measurement requires decoherence, so the process going on in this experiment would not be properly termed a "measurement", just an interaction between the photon and the beam splitter.
     
  10. Nov 29, 2016 #9
    I don't quite understand. In the second paragraph you say there is interference if the system is brought back into the state prior to measurement. I assume in this state there is the possibility of obtaining the path information (otherwise the measurement would have been pointless anyway). But in the first paragraph you say that there will be no interference in the presence of such a possibility, even if no measurement is performed?
     
  11. Nov 29, 2016 #10

    DrChinese

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    In my first paragraph: I draw the distinction of a situation where a measurement is clearly made, but the result is discarded into the environment. If you choose to ignore that information (or look at it), the outcome is the same. There is NO interference.

    In my second paragraph: I draw the distinction where a state is returned to the original. There is no lingering information available, either to look at or ignore. There IS interference.
     
  12. Nov 29, 2016 #11

    DrChinese

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    A. Neumaier might quite agree with this approach. I don't really object, and probably most would say the same as you. I still think it comes back to your definition. If you don't see a measurement and subsequent erasure (or reversal), there is no objective way for me to say it is there. We're back to the idea that speculating on the activities of quantum particles (when we are not obtaining information about them) is a bad idea.

    But I still see measurement and reversal. :smile:
     
  13. Nov 29, 2016 #12

    Nugatory

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    In both cases there is an interaction. But not all interactions are measurements, so we need an agreement about which interactions are measurements. If we consider that a measurement is a statistically irreversible interaction (a position that interacts nicely with decoherence) then the second case is not a measurement.

    So another question: Can the interference pattern be maintained across a statistically irreversible interaction? (Before the pattern itself forms on the screen - that's pretty clearly irreversible).
     
    Last edited: Nov 29, 2016
  14. Nov 29, 2016 #13

    atyy

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    Measurement is irreversible.

    Passing through a PBS, although colloquially may mean a measurement - strictly speaking it is not, since considering a larger system, the projection of the PBS can be modelled as unitary evolution. https://arxiv.org/abs/quant-ph/0305007v2
     
  15. Nov 30, 2016 #14

    OCR

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    Last edited: Nov 30, 2016
  16. Nov 30, 2016 #15

    atyy

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    Probably the other way - measuring and throwing away information is equivalent to decoherence which is unitary evolution (in principle reversible). It is only when a measurement is made and the information retained that state reduction is necessary.
     
  17. Nov 30, 2016 #16

    A. Neumaier

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    No. As long there is no measurement result (communicated by the interaction to the environment) there is no measurement in any meaningful sense of the word.

    But these are all unitary transformations, not measurements. The state remains completely unknown to the observer (unless it was known initially, in which case it remains completely known). But without information flow no measurement!

    I'd be interested in your definition of measurement that leads you to the opposite conclusion, and to a justification why what you call so deserved to be called a measurement although nobody can know anything about the measurement result.
     
  18. Nov 30, 2016 #17

    vanhees71

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    I don't know, about which concrete experiment you guys are talking right now. In the quantum-erasure experiment by Walborn et al that I mentioned above, of course very specific measurements of the polarization of photons are done and measurement protocols irreveribly fixed. These measurement protocols then allow to choose subensembles of the total ensembles such that putative which-way information is "erased" for this subensemble. It's a pretty easy to understand delayed-choice experiment without any surprise, if you are familiar with quantum mechanics, and it's very clear, how the interference pattern is restored for the subensemble but missing for the total ensemble. For a simple explanation in German, see

    http://theory.gsi.de/~vanhees/faq/qradierer/qradierer.html
     
  19. Nov 30, 2016 #18

    DrChinese

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    Nice reference, thanks. And yes, I agree that strictly speaking, a measurement is a measurement is a measurement.
     
  20. Nov 30, 2016 #19

    DrChinese

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    I'm not really disagreeing with everyone's final opinion. No information to the environment, no measurement. Context is king, you must look at the ENTIRE experimental setup to get the right answer.

    However, it does not take any special insight to see that a PBS does "something" within that greater context. Since the net result is "no measurement" and there are 2 component apparati, what is it that the PBS does? Obviously until the passing photon is measured as going through one branch or the other, the potential is not actualized. So the irreversible detection is the space-time point of where/when the measurement occurs, and that is by definition - making it impossible to have a different opinion if we all agree on that word's exact meaning.

    But as always, that means that it is the later detection (or not) that determines the nature of what happened at the PBS earlier (and that no "measuring" occurs there). This makes perfect sense to me, precisely because I agree that context is king. It does seem to me an abuse to pretend that nothing happens at the PBS or the reversing PBS. What do you call it if not a conditional measurement or the like?

    Again, to me there is no disagreement about the physics. If we specify the context, we will agree on the expected outcome. I don't think the words are particularly effective in describing that, given the example and others like it.
     
  21. Nov 30, 2016 #20

    DrChinese

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    You can return it to the earlier state without knowing what it is, right?
     
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