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Reading about the DCQE experiment commentary by Ross Rhodes.

My question is: why can't information about the future state of the idler photon (the one that heads toward the Glen-Thompson prism) be gleaned from the D0 detector in order to enable "predictions" of the future?

I'll preempt any "because that would violate conservation of quantum information" responses by saying, yeah, that's why I'm asking this question. I'm certain there is something I don't understand and I'm hoping someone can help me understand it.

I've seen these other questions:

Can post-selecting on the screen in the Delayed Choice Quantum Eraser experiment be used to predict the quantum-eraser measurement results?

Delayed Choice Quantum Eraser: Am I missing something here?

Delayed Choice Quantum Eraser?

Delayed Choice Quantum Eraser without retrocausality?

Are photons locked in time, and does this explain the "delayed choice quantum eraser" experiment?

Either none of them answer the exact question I'm asking, or (more likely) I'm not understanding the answer. I'm sorry to drag people through the explanation again, I'll do my best to propose a simple modification to the experiment which you can tell me the outcome of, your answer will help me understand.

Since DCQE seems to have a tendency to attract magical thinking (myself included), hopefully, this can be asked and answered clearly enough to dispell the magic and uncover the mechanics.

The experimental setup is this: Delayed Choice Quantum Eraser

A photon is sent through a double-slit where it passes randomly and then is split into two entangled photons. The upper entangled photon (signal photon) hits the D0 detector where its x position is recorded. The second photon (idler photon) goes down to the lower part of the diagram where it either is reflected into D3/D4 by BS (which gives us information about its path) or it passes through to another reflector (unlabeled in the diagram) that destroys its path information.

If that explanation doesn't make sense, here is a video that explains the experiment. Fair warning, it devolves into magic at the end, but prior to that, I found it to be helpful.

Whenever a photon is detected by D4 or D3 we should get a "clumping pattern", rather than an "interference pattern" (that's the terminology used in the video, I don't know if it's correct) because we know about the photon's path. If it hit D4 then we know it came from the lower slit (blue line) and if it hit D3 it came from the upper slit (red line).

The Grand Reveal, amazingly, is that the result from D0 will also show that clumping pattern! Somehow, even though D0 happens before D4 or D3 it "knew" that its entangled twin was going to be detected before it even happened.

I know, I know, this is where the physicists on this site are snapping their optical nerves with vigorous eye-rolling. I'm guessing this is where the break in my understanding is.

The reason I think this is an error is that if it were true DCQE could be used to create a future predictor, which either means all the quantum physicists in the world should already be billionaires, or I'm missing something (I wonder which one).

To demonstrate this, here is the same experiment with only the eraser (I removed BSa and BSb and labeled the final reflector BSc):

Eraser Mode

Quantum Eraser (Only Eraser)

Let's call this Eraser Mode since all it does is erase our knowledge.

In the top-right corner, I have connected the output of the D0 detector to a monitor where we will plot the x impacts.

If the video and (my reading of) the commentary are correct, then since I do not have information about the path that the photon took, I should see an interference pattern on the ${Output}_{Erase}$ display.

This, I'm guessing, is not true and is another hole in my understanding. Rather, the Coincidence Counter must be what enables the creation of the interference pattern, but the article seemed to indicate that the detector itself shows that pattern.

Here is the experiment again, this time with just the Eraser removed (the one I labeled BSc) and only the signal reflectors remaining:

Signal Mode

Quantum Eraser... without Eraser

Let's call this Signal Mode since regardless of how the experiment plays out we can figure out which slit the photon went through (D2 or D3 is bottom, D1 or D4 top).

I've also connected the output of this system to a display named ${Output}_{Signal}$.

The question is this: Will the output of ${Output}_{Signal}$ look any different than the output of ${Output}_{Erase}$?

It could be an interference pattern (artist's rendition, be gentle):

Interference Pattern

Or no interference pattern:

No Interference Pattern

Or something else, because I don't understand.

The problem is that if there is a different pattern on ${Output}_{Signal}$ than there is on ${Output}_{Erase}$ then I could use that to predict the future.

Quantum Predictor

I could set up a delay mechanism between the Glenn-Thompson prism and the BBO so that it takes a long time for the photon to make it to the prism. Let's say I send it through 120,960,000,000 km of fiber optic cable (a cable so long that it could go around the equator >3 million times) so that it takes a week for the photon to make it from the BBO to the prism (assuming the speed of light in the cable is 200,000 km/s). In the meantime, I can measure the pattern on the D0 detector.

If I have switched the lever to the Signal State, then BSc is removed and it will only show the non-interference pattern. If instead, I switch it to the Erase State then the BSa and BSb are removed and it will show me the interference pattern.

If I see that the output is an interference pattern I can conclude the system will be in the Erase State when the photon arrives in a week. If I see a clumping pattern I can conclude the system will be in the Signal State when it arrives in a week.

Of course, then I can get up to all sorts of shenanigans by, say, writing a script that flips the switch if Bitcoin ever goes over 10k in that week (or whatever).

This future prediction trick makes me pretty sure that my understanding is incomplete. In particular, I think the gap is in understanding how the coincidence counter uses the incoming data to create the interference pattern.

If that's the case, then I'm not that impressed by this experiment. I mean, essentially it's saying, "From the parts of the system where we have more information, we can get more information about the system." Or am I also missing something there?

Probably the easiest way to answer this question is to tell me what pattern I will see at the D0 monitor.

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    $\begingroup$ If you've read popular articles that say the delayed choice quantum eraser can affect the future or the past, I'm sorry, but you've been duped. Please forget everything you have been told -- it is literally worse than knowing nothing at all. $\endgroup$
    – knzhou
    Oct 25, 2019 at 5:55
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    $\begingroup$ Lots of people working in physics know perfectly well that this is a horrible way to explain what is going on, and almost precisely the opposite of the real point of the experiment -- but a minority of physicists, some journalists, and a bunch of cranks, enjoy sounding mindblowing more than being straightforward. $\endgroup$
    – knzhou
    Oct 25, 2019 at 5:56
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    $\begingroup$ But if you describe the experiment with casual language, treating the photons as if they were classical bullets, then you cannot get the right answer out unless you invoke magical backwards causality. That's not a proof that QM does that -- it's a proof that trying to talk about QM as if everything is secretly classical is a really really bad idea. You need to put in crazy complications that, if literally true, should ruin our ability to do any science at all. $\endgroup$
    – knzhou
    Oct 25, 2019 at 6:03
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    $\begingroup$ @knzhou Yeah, I figured. That's why I'm seeking clarification here. Take this as you helping to innoculate one more person against bad ideas so that I can help contribute to herd immunity :) $\endgroup$ Oct 25, 2019 at 6:06
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    $\begingroup$ You are right that the coincidence counter is key. If you just look at the output of D0 directly without the coincidence counter, you will see all the photons that ended up at D0. So, interference pattern and clumping pattern superimposed. To see either the interference or clumping patterns, you need to connect D0 up to the coincidence counter and sort out which photons at D0 had their "partners" end up at D1/D2/D3/D4. If you pick out just those photons whose partners ended up at D3/D4 (which you can only do after both photons arrive), you will see the interference pattern. $\endgroup$
    – d_b
    Oct 25, 2019 at 6:08

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You are misunderstanding what information you get from each of the sensors. And by information I mean the peaks and troughs in the image formed by the photons, that can be further interpreted by humans. The first axiom I want you to take is D0 = sum(D_i), meaning that the information (peaks and troughs) at D0 is the sum of the information of all sensors detected using the idler photos.

It does not matter what you do to the idler photons, the output of D0 in both cases (Signal Mode and Eraser Mode) will be this:

In the case you turn on Eraser Mode and you check the photons of D0 that hit R01 = D1 or R02 = D2 you will get this:

enter image description here

Take a look of how R01 and R02 are dislocated from one another. If you add both signals together, you get R01 + R02 = D0. Notice how the peaks of R01 align with the troughs of R02, such that the final result is the value in D0. This mode results in an interference pattern only because you can sort between the photons of each sensor.

If you now switch to the Signal Mode, such that R03 = D1 + D4 and R04 = D2 + D3, this is what you will get:

enter image description here

In the same way as before, if you add R03 and R04 you will get D0, but in a different way from the Signal mode. And by "different way", I mean that now there is no interference pattern. You see no interference pattern since the phothons are concentrated around one location (one peak for each slit/sensor).

As you can see, looking at D0 will not help you get any future predictions, since it will always yield the same result, no matter what you do to the entangled photon. The patterns only emerge after the coincidence counter sorts which photon went to each sensor.

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    $\begingroup$ Do you know where I can find the actual code that’s used in the coincidence counter? $\endgroup$ Oct 22, 2020 at 11:04

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