What Prevents Delayed Choice Quantum Eraser Experiment from Being Used to Predict the Future?
Reading about the DCQE experiment commentary by <PERSON>.
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:
https://physics.stackexchange.com/questions/480062/can-post-selecting-on-the-screen-in-the-delayed-choice-quantum-eraser-experiment
https://physics.stackexchange.com/questions/214777/delayed-choice-quantum-eraser-am-i-missing-something-here
https://physics.stackexchange.com/questions/323678/delayed-choice-quantum-eraser
https://physics.stackexchange.com/questions/343121/delayed-choice-quantum-eraser-without-retrocausality
https://physics.stackexchange.com/questions/507259/are-photons-locked-in-time-and-does-this-explain-the-delayed-choice-quantum-er
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:
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. 617
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
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. 795