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

I'm curious about QM and spent the last 3 days thinking about Delayed Choice Quantum Eraser (DCQE) experiment, but I couldn't solve this issue:

1. Assume we do the DCQE experiment so that for the whole experiment (let's say, 1000 particles) finishes before the first particle reaches the detectors 1-4 (using the notation from this diagram from Wikipedia).

2. Assume also we're using a switch to control if the idler particle goes to which-way-detector or to the eraser.

3. This schematic shows what we should see in $$D_0$$, even though we don't know yet $$R_{01-04}$$

4. Now, knowing $$D_0$$, use the switch to send the 100 particles that reached the most-left side of D0 to the eraser detectors ($$D_1$$ and $$D_2$$). It seems much more likely that they reach $$D_2$$ than $$D_1$$, because it's on peak on $$D_2$$ (and on rest on $$D_1$$) even though it's going through a half-silvered mirror. This looks like a contradiction to me.

So, am I missing something or QM is just that weird?

• You're over-interpreting those plots. They're schematics, and three details are not accurate to the level required for the interpretations you want to hang on them. May 14, 2019 at 21:47
• Isn't it true that the patterns made by the particles that reach R01-04 follow distinct distributions on D0? If so, it seems reasonable to extrapolate that there are some regions that are inverse peaks for D1/D2. May 14, 2019 at 21:55

You're over-interpreting these sketches - they are only sketches, and their specific details can't really be used to make any real predictions.

Here is a more accurate version of those sketches, with a proper underpinning on a solid model of the experiment's behaviour:

Mathematica source via Import["http://halirutan.github.io/Mathematica-SE-Tools/decode.m"]["https://i.stack.imgur.com/P6HYG.png"]

As you can see "the leftmost part of $$D_0$$" is equally compatible with the patterns $$R_{03}$$ and $$R_{04}$$, as detected on the quantum-eraser detectors 1 and 2.

Still, you're not entirely wrong, particularly in the sharper formulation you give in the comments:

Isn't it true that the patterns made by the particles that reach R01-04 follow distinct distributions on D0? If so, it seems reasonable to extrapolate that there are some regions that are inverse peaks for D1/D2

Yes, the patterns made on the $$D_0$$ screen when post-selecting on $$D_1$$ and $$D_2$$ detections are indeed different - and, in fact, they're complementary interference patterns, with the peaks on $$R_{01}$$ lining up with the troughs on $$R_{02}$$ and vice versa. (This is how they can add up to an interference-less $$D_0$$ pattern when there is no post-selection. It is crucial that you understand that both $$R_{01}+R_{02}$$ and $$R_{03}+R_{04}$$ add up to $$D_0$$, and what that means - the 1/2 and 3/4 pairs are just different ways of splitting up the $$D_0$$ counts, depending on information acquired later.)

This means that you can zero in on one of the peaks of the $$R_{01}$$ fringes, say, the green box below:

If use some fancy switching mechanism to ensure that you send all the particles that fell on that green box over to the $$D_1$$/$$D_2$$ quantum-eraser part of the idler-photon side of the experiment, then indeed, as you say,

it seems much more likely that they reach D1 than D2.

Is this a problem or a contradiction? No. The photons are not going through an arbitrary half-silvered mirror - they're going through a precisely calibrated beam splitter. The beam path that reaches $$D_2$$ includes a contribution from $$M_b$$ (red beam) and a contribution from $$M_a$$ (blue beam), and if those beams are coherent, they can interfere both destructively and constructively. Absent any information about what happened to the signal photon on $$D_0$$, the idler and the signal are entangled, and there is zero relative coherence between those two beams, and $$D_2$$ will click half the time. However, by post-selecting on $$D_0$$'s measurements on the green box, you're effectively fixing the phase between the two beams in such a way that they interfere destructively on the $$D_2$$ side (and constructively on the $$D_1$$ side), so no light goes through to $$D_2$$ (on those post-selected runs).

So, basically, what you've described is a fancy way to run the quantum-eraser apparatus in reverse, where by splitting the $$D_0$$ screen into sectors you're providing information that can be used in a post-selection scheme to recover the interference pattern that comes out of the BS$$_\mathrm{c}$$ beam splitter.

If that seems weird, then yes,

QM is just that weird.

• Thanks very much for taking the time to answer my question, that's a great explanation! Indeed it was wrong to assume the beam splitter was a an arbitrary half-silvered mirror; they wouldn't interfere constructively/destructively if that was the case. May 14, 2019 at 23:46