Solving the Delayed-Choice Quantum Eraser

This video gives a detailed explanation of how to correctly interpret the delayed-choice quantum eraser. This is followed by a full derivation of the equations that describe the problem. If you find these steps a bit rushed, I suggest pausing the video after each step.

*CORRECTION*: around 15:16, there is a small typo in the expression under “Replacing wavefunction past BS”. The term |ψ⟩ᵗᵢ at the end of the equation should not be present.

The derivation uses a combination of the following sources:

[HadiLq]

It takes twenty years for us to notice we have an interferometer instead of an eraser.

[BattleAngel-mmxt]

Thank you a lot! I've been following this experiment since I watch it first time back in 2015, trying to understand it thoroughly. I didn't quite understand why in the debunked videos of this year they don't explain the actual root cause of the interference. Finally I can understand it, especially in the explanation at 10:00 🙏 you are the hero man, thx for the video

[JoseMoreno-ko]

Well, the circuit that you present at the end does not correspond to the "delayed-choice quantum eraser experiement" (DCQEE); it is presented simply as the "eraser" in the literature (although you can include a "delay"). Keep in mind that in the DCQEE, the quantum system itself "decides" the type of pattern that they will become, that is, either an interference pattern or not. In the circuit that you show, YOU decide the type of pattern, that is, the circuit would need extra qubits to make sure that two types of pattern are automated by the quantum system. If that circuit that you show at the end can be called a DCQEE just because of a "delay" in the measurement of one of the qubits, then you can also call a Bell-type of experiment a DCQEE when a "random" strategic measurement is performed after the other, by a the researcher, faster than the time that it would have taken the information to travel between the detectors, that "erases" whatever information was detected in the first, such that the outcomes "violate" a Bell-type inequality. Notice that in the latter case, it is not as simple to explain the outcomes in terms of "instructions" that can be set from the start, which is really what the DCQEE should have been about given that it was an attempt to show the "spookiness" of quantum systems where retrocausality is just another interpretation among so many others.

If you really want to make the analysis more intuitive so that one does not have to resort to retrocausality, you could just say that the experiment results in correlations of measurement, not causations of one on the other, given that "coincidences" is what is being measured at two space-like separated locations.

[jeffweyenberg]

Well done sir! The best explanation of the Quantum Eraser on the internet

[jorgelbc]

The best explanation I've found so far on this subject. Thank you very much.

[DaGhost]

Great video! I'm still wrapping my head around all this, would the following be correct?
- D0 shows a clump pattern because its function is the sum of the two wavefunctions/photons generated through the BBO crystal. So no interferences takes place since it's not just one wavefunction interacting with itself, but two incoherent photons.
- Regarding ~6:12: the first measurement collapses the wave function leading to in this case D0 determining the outcome of D1-4. If D1-4 would be the first measurement, it would lead to the proabililty of D0 being "fix" through quantum entanglement.
- if I were to put a screen at D1/2 an interference pattern would be visible but not from the fact that the particle's wave interacted with itself but rather from the fact that the measurement there combines both upper and lower particle information.

[erinm]

This is an incredible video! I finally allllmost get it. Other debunking/explanatory videos have skipped over anything having to do with correlations between locations on D0 and the various other detectors, and so have been wholly unsatisfying. Your video gets me by far the closest to understanding!

The remaining confustion I have can be summed up this way. Around 4:20, you say the BBO crystal splits the waves from the top and bottom slits into two separate, isolated branches of the global wave function that cannot interfere with each other (hence no interference pattern on top screen).

Then around 9:30, you say that the information photon will still carry the probability amplitudes of having gone through the top slit or the bottom slit, and it appears that the beam splitter recombines these two wave probabilities, and the two waves interfere with each other, making certain screen locations correlate with the chances of landing at D1 or D2. But doesn't this contradict the idea that the two beams are in different branches of the wave function that can't interfere with each other? I think I'm missing something about how the information photon caries the probability information, that would make this more clear.

[andruss]

Thanks! Looks like the famous Quantum Eraser Experiment is a kind of failure. But what about retrocausality, demonstrated in John Wheeler's Delayed Choice thought experiment? Is it valid? According to Australian National University web article, they made a version of it, that was tested in real life and it works as described by Wheeler (retrocausality works). If this IBM Quantum Computer would be also able to simulate this experiment, and you, Diego, someday decide to make a video of it, that would be great. "At the quantum level, reality does not exist if you are not looking at it" (ANU Professor Andrew Truscott)

[robinfinesmith]

Is anyone here familiar with the book by Ananthaswamy? Does this video imply that the representation in his book of the quantum eraser is factually wrong?

[Existidor.Serial]

No matter how hard we try, we wont be able to fuck up the universe.

[inCred]

Hey everybody, can someone explain why the two branches of the wavefunction hitting D1 and D2 have opposite relative phases? In other words: why is there a plus at the top branch and a minus at the bottom branch? I mean, all ways to D1 and all ways to D2 are the same. I do not see any difference in the geometry of this experiment

[ckmfunk]

I like the video and I think all you say is perfectly fine, but you seem to downplay the interesting part: the D0 photon must "know" where to land based on something that will only happen in the future, even though nobody can ever use this "knowledge" because there is no communication nor causation (only the correlation with a future choice of the setup).

[bizarre]

So the interference @ D1 or D2 is the consequence of 90-degree phase shift of beam splitter?

[JohnKNMurphy-nz]

My experience is in solid-state physics and optoelectronics, so I'm not an expert in quantum computation and am hoping to learn more. In the actual photon experiment, an essential component is the Glan-Thompson (G-T) prism straight after after the BBO. Surely that prism forms a type of quantum gate that processes the photon pairs into orthogonally polarized states. Nobody seems to talk about the implications of this in discussions of this experiment, and yet it seems to be a crucial part of discussing how it works in quantum terms. Before the G-T we don't know the relative polarization along each path, after, we do. Surely it adds another Q-bit to each path.

[motor]

This is brilliant. Peeking into super-posistions always gave me a sensation that we're looking at cheat codes for ether creation 😊 Just for a while I had my own ideas just being a small lad about the functions of subatomic phenomena, just wasent able to put an idea towards the visual, growing up; these things slowly started to make sense to me through physics lectures, reviewing formulas to equations and finally seeing more demonstrations solidified. Physics is my infinatum. 🙂But not beyond my dreams.

[PsychoMuffinSDM]

Interesting. I’ve watched a lot of these kinds of videos, and this one does the best job so far I feel. I feel like if I go through that math, it’ll be a bunch of alg and trig identities. Which kinda helps explain it, but it that “cause the math says so” kind of explanation.
I’m still confused why one pair sorts into a interference pattern, and the other doesn’t. I’ll need to watch this a bunch more times.

[Killer_Kovacs]

That means the quantization it dependent on the particles orientation on the wave

[yorailevi]

This is actually an important experiment not because of the pattern on the screen but because of the statistical interpretation that arouses based on the questioning bias

[hineang]

so how come the wave doesn't collapse when it hits the space between the slits?

[apateon]

Great video! The first I heard about this experiment was around 2016 and it has haunted me ever since. For someone with zero academic background on quantum mechanics, all of the debunking videos I've watched only added more to my confusion. Thanks to you I've cleared my misconceptions.

This might be outside of the scope of this video, but one thing caught my mind. So far what I understand is that the beam splitter "decides" whether the photon goes into D1 or D2 based on their relative phase difference hence the interference pattern. And that a "fair" beam splitter would not results an interference pattern. But what's the mechanism behind this beam splitter? Why does the constructive interference go one way while the destructive goes the other way?