Why do quantum eraser and original double-slit setups produce different patterns on the detector?

Question

A similar question has been asked here, but there was no answer: Why Delayed choice quantum eraser doesn't produce two lines

I learned that in the original double-slit experiment, an interference pattern is observed after firing many photons on the detector.

I also learned that in Delayed-choice quantum eraser experiment, when you look at the detector, what you initially see is just noise. Only after separating out the photons according to which detector detected their entangled pair, you start to see interference patterns on D₁ and D₂ detectors.

What I'm wondering is what causes the interference pattern seen on the main detector in the original double-slit experiment to turn into noise in the quantum eraser experiment. I am suspecting it's because the beam splitter BS_C but I don't understand why.

Let's consider a simpler experiment than quantum eraser, removing the two initial splitters BS_a and BS_b. The photons travel from both paths and which-way information is deleted when they pass through beam splitter BS_C.

What do we see in the detector D₀? Interference pattern or noise? If noise, why? In the original experiment we saw interference pattern, what caused the difference in this case? Since we removed the information, I would expect the result to be equivalent to the one in the original experiment.

In other words, I don't see a difference between this experiment and original experiment, other than the fact that we have entangled photons here which doesn't provide any information thanks to BS_C. Why is the outcome different?

Thanks!

Answer 1

There's no way to affect the observable behavior of the "upper" photons by manipulating the "lower" photons after the initial generation of the entangled pairs in the Glan-Thompson prism (if there were, you could use it to send a signal faster than light).

There's no interference pattern because the lower photons contain which-path information about the upper photons. Even if you never measure that information, its presence in the world prevents visible interference. There's no way to destroy the information except by reversing the process that originally created the entanglement, which is impossible in practice in this setup.

This answer has a more detailed discussion of a different version of this experiment. The key point is the same: if information about the light is preserved elsewhere in any form then there's no interference, and that information can't be and isn't destroyed, despite the name "quantum eraser".