About the delayed choice quantum eraser experiment

[Srullic]

Hey, I was watching this video

About the quantum eraser experiment (I suggest you watch too, so we would be speaking in the same terms). As I understand it, The experiment goes such that:
first the photon enters through the slits as a superposition,
then the photon gets measured to gain which-slit information (via its twin brother, as explained in the video),
and then the superposition 'collapses' to a single state (according to the which-slit information), and the photon reaches the screen.
The result, after many trials, is no interference. No future-affects-the-past business here.

So my question is, what if we run the experiment the following way: Suppose that you could trap the twin brother of the photon that goes through the experiment, for as long as you would like, without measuring it (I have no idea if that's practically possible). So you fire many photons at the screen, get your pattern, and then measure each photon's twin. Are you still going to get a no-interference pattern?

If so, I could imagine a way to send signals to the past. Say your measuring device measures the twin photons only if some dice rolls a six. If the dice rolls a six after we get our pattern, the pattern has to be no-interference, and thus we could conclude that the dice rolled a six before it was rolled!

So my questions are:
1. What does the theory dictate should happen?
2. Is this experiment actually practically possible?
3. If so, has it been done?

Thank you for your time.

 

[vanhees71]

But the quantum eraser experiment (I cannot watch the movie right now) is right what you describe. You store the results of the measurement of the idler photon. By only using part of the total ensemble by looking only at the signal photon for which the idler photon was found in one specific polarization state, you destroy the which-way information and the paritlal ensemble of photons show the interference fringes, which the total ensemble doesn't show.

 

[Srullic]

Well, I only just heard of this experiment (I guess 'idler photon' mean the twin photon? And I'm not sure what 'partial \ total ensemble' means at this point...).
From what I watched in the video, the time interval between the photon entering through the slits and the photon being measured is very short, such that the photon hits the screen after the measurement collapsed it into one state. So it's not surprising that what we get is a no-interference pattern.
My question is about lengthening that time interval for as much as we like. If the results are really the same (we get no interference), doesn't that mean we could send signals to the past (as I described above)? I mean, obviously not, otherwise we'd be doing that already. What am I missing?

 

[Strilanc]

You always see a lack of interference pattern in DCQE experiments, regardless of the choice. You only find interference patterns after the fact by manually grouping the spots on the screen, based on the detector that the associated idler photon set off.

Furthermore, thinking of it as the idler photon after-the-fact affecting the photon that hit the screen is thinking about it backwards. We're dealing with correlations, not cause and effect. The ordering really doesn't matter at all. The landing point on the screen tells you how the "choice" measurement will play out just as much as the choice measurement outcome tells you how the landing point will be biased.

 

[Srullic]

Well now I'm more confused. I looked at the wikipedia page about the experiment, and it did show these graphes, and stated that you always get a lack of interference pattern. But the experiment as described on the page seems different than the one described in the video (there are four detectors for some reason, and there's no talk about polarization), and I feel like the results of this experiment don't help me understand the scenario in the video.
The experiment I was talking about was described like this:

A photon has four polarization states: horizontal (h), vertical (v), clockwise (c) and anti-clockwise (a).
a photon with polarization h or v goes through a double slit, that has a mechanism that changes the polarization of the photon in the following way:
If it went through the right (R) slit, then h->c, v->a.
If it went through the left (L) slit, then h->a, v->c.
The polarization of the photon is measured at the screen. The polarization gives no information about which slit it came through (if we measured c, it could have been h going through R or v going through L). As such, we are uncertain about which slit each photon came through, and we do get an interference pattern (that's the part which you say is wrong. Why is it wrong?).
But let's say before we send the photon through the slits, we (somehow) create an entangled twin of it, such that if the photon is h, the twin is v, and vice versa.
we send the photon to the slits, and the twin to a device that measures its polarization. Now knowing the polarization of the original photon tells us which slit it came through (if we measure c for the photon and h for the twin, then the photon was previously v and as such must have gone through L). As such, we know which way each photon came through, and we don't get an interference pattern.
This result is the same regardless of when the twin photon was measured.

So the part that is wrong about this is the part where we get an interference pattern on the screen if we don't measure the twin? Are there any other parts that are wrong?

 

[Strilanc]

A photon has four polarization states: horizontal (h), vertical (v), clockwise (c) and anti-clockwise (a).

The polarization of a photon is a two-level quantum state. A qubit. The clockwise and anti-clockwise states (as well as the diagonal states) are superpositions of the horizontal and vertical states. This is important: it means you can't 100% distinguish between H and C, since C is just H+iV or whatever.

So you might say a photon's polarization has two states, or that it has a continuum of states living on the surface of a 2d sphere (the Bloch sphere), but definitely not four.

a photon with polarization h or v goes through a double slit, that has a mechanism that changes the polarization of the photon in the following way:
If it went through the right (R) slit, then h->c, v->a.
If it went through the left (L) slit, then h->a, v->c.

This entangles the polarization with the path. It's equivalent to rotating the polarization by 90 degrees only at the right slit. It's equivalent to hitting the polarization qubit with a Controlled-NOT controlled by the path.

You will not see an interference pattern in this situation, unless you have polarized light coming in and plop the correct polarizing filter right in the middle of the experiment (between the slits and the screen) (the filter does the group-and-only-look-at-one-of-the-groups part for you; if you use its opposite you will see the other group).

and we do get an interference pattern (that's the part which you say is wrong. Why is it wrong?).

The video doesn't say that. It doesn't even mention the setup you described. Where are you getting this from? I bet they have that polarizer-in-the-middle that I mentioned.

the twin to a device that measures its polarization. Now knowing the polarization of the original photon tells us which slit it came through (if we measure c for the photon and h for the twin, then the photon was previously v and as such must have gone through L). As such, we know which way each photon came through, and we don't get an interference pattern.

Right, you won't see an interference pattern with this setup.

 

[zonde]

Well now I'm more confused. I looked at the wikipedia page about the experiment, and it did show these graphes, and stated that you always get a lack of interference pattern. But the experiment as described on the page seems different than the one described in the video (there are four detectors for some reason, and there's no talk about polarization), and I feel like the results of this experiment don't help me understand the scenario in the video.

There are wikipedia pages about Quantum eraser experiment and Delayed choice quantum eraser. Video describes Delayed choice quantum eraser but when you talk about polarization it sounds like you have looked at Quantum eraser experiment page. So can you give a link when you talk about some wikipedia page?