During what points can quantum information be erased in the delayed choice experiments?

I looked for these specific questions in other threads, but I couldn’t find them. I was wondering if anybody knows of someone doing a couple of variations on the 2000 Kim et al. experiment. I’ll refer to the wikipedia description of the experiment, so when I refer to specific splitters, detectors, etc., those are in reference to the corresponding diagram in that article.

The popular explanation of such experiments is “if you erase which-path information, you get an interference pattern.” It seems to me, though, that there’s more than which-path information that needs to be considered in the question of interference. The data itself doesn’t seem to support that assertion, since the interference patterns achieved through coincidence correlations at D1 and D2 exactly complement each other, such that if you were to overlay them you’d just get a blob.

This suggests that it’s not just about preserving or erasing which-path information. There’s a more fundamental quality (coherence) of interferability itself, that needs to be detected so that the “right” photons can be used in the experiment. Specifically, the slit A photons that are reflected by BSc seem to form an interference pattern with the slit B photons that are passed by BSc, and vice versa.

So, here’s the variation this suggests:

  1. Get rid of BSa and BSb, along with D3 and D4. These are premature. At this point, the results seen by counting coincidences between D0 and D3 or D4 should not change from the original experiment. (It wil just happen faster because more photons are getting through.)

  2. Change the angles of mirrors Ma and Mb, so that the “slit A” beam and the “slit B” beam diverge as they go through BSc. Then, add mirrors in all paths so that the original correlated path lengths are the same again, and meet back at the original detectors. This should also not change the experimental results. (Unless the angle of incidence against BSc is relevant to getting the coherence right.)

  3. (and here’s the first crux): Remove the additional mirrors that cause the divergent paths to arrive at the same detectors, and instead re-introduce D3 and D4, but this time in a position to pick up the additional paths. It doesn’t look like there’s a way to post pics, so hopefully it’s clear what I’m talking about.

Here’s the first point where different interpretations should yield different results. Looking at an interpretation that the article claims is valid:

If this is the correct interpretation, then consider the photons, under varation #3 above, that came through slit A and passed through BSc (let’s say these are detected by the new D3) along with those that went through slit B and were reflected by BSc (let’s say these are being detected by the original D1). Under the interpretation above–what I think of as the “probability filtering” interpretation–the combination of D1 and D3 coincidence with D0 should yield an interference pattern at D0, while D1 and D3 each on its own should yield some part of an interference pattern. But under the popular explanation, D1 and D3 would yield only blobs.

So, has anybody done a variation like this?

Now, suppose that somebody does this variation and finds that D1 and D3 yield blobs, as the popular interpretation of quantum erasure indicates they would. There’s one more variation that would be interesting, and this is the part that goes to the title of my post:

  1. What if, under variation #3, after the encoding of a photon incidence into an electrical pulse (or whatever it’s encoded as), the electrical pulses from D1 and D3 are combined into a common, same-length path before coincidence counting?

If the relevant act in these experiments is really the erasure of which-path information in one stream before it can be correlated with the other stream, then variation #4 should yield an interference pattern.

If not, however, then this suggests another interpretation of the original results (at least of the Kim experiment), which is this: That the photons of the two streams (slit A passed by BSc and slit B reflected by BSc, or vice-versa), when brought together in the same (or nearly the same) location for detection, interfere with each other in either a reinforcement or cancellation manner, as the simple quantum eraser in the wikipedia article describes. (Even though those photons arrive one at a time.) The position of D0, and the slit A and slit B photons arriving there, has a correlation to whatever properties in the two beams, after encountering BSc, would cause them to reinforce or cancel each other.

Under that interpretation, it seems to me that the weirdness still stops with photons interfering (in a cancelation/reinforcement manner) when fired one at a time. Everything else about the delayed choice double-slit quantum eraser experiments seems to be a matter of just selectively filtering which photons you look at. I don’t see, in the experiments that I’ve read so far, that there’s a reason to conclude that the filtering doesn’t operate on properties that already exist in the photons at the time they’re emitted. When you filter the right set, you get interference. (In other words, entanglement, while interesting, still doesn’t seem to imply either “spooky action at a distance” or “reverse-causality.”)

So there’s one more variation:

  1. Instead of #4, start with #3 (observing the “blobs”) but replace D1 and D3 (which are in separate locations) with a single, larger detector that can equivalently detect both sets of photons. (Is this possible?) What would the accepted models of quantum eraser experiments predict in this case? The which-path information is preserved in the location on the detector that the photon hits, but the detector itself doesn’t have a way of distinguishing or reporting that. (I don’t think it necessarily changes my proposed interpretation, but it seems it would still be an interesting half-way step between #'s 1 and 4).

Are there any experiments that have already measured the results of my proposed variation #'s 3, 4, and 5?

Thank you for any information.

Nobody knows of anyone bothering to /really/ investigate the informational/observational interpretation of some of these quantum experiments?

It is really difficult to follow exactly what you are trying to achieve, the phase shift of π between R[sub]01[/sub] and R[sub]02[/sub] is caused by BS[sub]c[/sub]. This is a well-known property of beam-splitters. Also remember single photons are being passed through the set-up one at a time so that those photons going through slit A and those going through slit B cannot interfere with each other (at least not in a way that can be classically understood).

This experiment is not set-up to demonstrate the non-local nature of entanglement, so you would not expect to see direct evidence of so-called “spooky-action at a distance”, that can be inferred from the theory and the Bell test experiments that have been performed.

The philosophical implications of the experiment are very much down to a matter of interpretation. For example Bohmian mechanics the particle unambiguously travels a single path, but the experimental set-up itself affects the quantum potential causing the differences between R[sub]01[/sub]/R[sub]02[/sub] and R[sub]03[/sub]/R[sub]04[/sub].

OK, so the experiment really doesn’t demonstrate anything more than that entangled photons have comlementary properties? Why does the wikipedia article call this out as a “delayed choice” eraser? I thought the purpose of “delayed choice” was to demonstrate non-locality qualities of entanglement.

You made the point that in this experiment the correlation between the entangled photons could be explained classically as due to pre-existing properties. This set-up doesn’t demonstrate either way whether that is the case (it cannot be demonstrated for single pairs of orthogonal entangled photons), however it is well-known that quantum mechanics says this is not the case and that the predictions of quantum mechanics cannot be re-created by such a local hidden variables (Bell’s theorem) and those predictions that cannot be re-created by a LHVT have been demonstrated experimentally by so-called Bell test experiments such as the Aspect experiment.

I thinks it’s astounding and credit to our members (Asympotically fat specifically) you got an answer at all for such a narrowly focused question. I am curious why in the world you posted this here vs some physics oriented message board. It seems you would get a much better chance of an answer there than a general knowledge Q&A board like the dope.

[astro], yes, kudos and thanks to Asympotically fat for the answer. I struggled with going somewhere like Physics Stack Exchange, but that’s an exchange point for active researchers; I’m just a curious lay person and I felt it would be overly presumptuous to ask questions directly there.

However, SDMB’s are for everybody, and a google search of related terms showed that there /are/, indeed discussion threads on questions related to quantum physics.

[Asympotically fat], you’ve given me another lead to pursue in my curiosity. I had read about one Bell-state quantum eraser experiment about two years ago, and in recent weeks I’ve been unable to find a description of the experiment that I first read about. It seemed to me that it was also explainable in local hidden variable terms, and I’ve been looking for it so that I could pick up my original line of thinking. But your reference to the “Aspect experiment” is a lead I can chase.

But my real question, here, was whether the quantum mechanical understanding is that the which-way information is resolved at the point when the photon strikes the detector or at the point when the resulting electrical pulse is coincided with the corresponding pulse from the other detector? In other words, if you have a setup where information is seemingly resolved at photon detection, does quantum mechanics provide the opportunity to erase it again in the resulting electrical field wave front traving through the wires to the coincidence counter? (Another way of asking it might be, do the quantum qualities in the photon persist into the electric field propagation in the wire?)

In any case, thanks for your answer, and for pointing me to another term to look for. Do you know of any physics forums or message boards that I could pursue such questions on? (That real physicists don’t mind the bumbling understanding of people like me?)