quantum mechanics - "Entangled photons never show interference in the total pattern without coincidence count" implies FTL

In my previous question, the most defended objection to the gedankenexperiment was that "Entangled photons never show interference in the total pattern without coincidence count".

Here I show another gedankenexperiment where if this affirmation is true then FTL communication is possible.

Assumptions:

• Alice and Bob have a 100% bright entangled photon source



• Alice and Bob's photons are 100% correlated in their polarizations


• Alice and Bob are in spatially disconnected and separated regions


• Alice and Bob have perfectly synchronized clocks


• Alice and Bob know exactly how far away they are from each other

The experiment is:

1. Alice generates a lot of entangled photons (10k for example), sends 1 photon of each pair to Bob and keeps the other photon to herself.


2. Alice keeps her photons undisturbed in some way, could be a mirror in the middle of the path towards Bob. In the diagram I represented it as a "looping device"...


3. Bob's photons take their time to reach Bob's apparatus



4. When the photons reach Bob's apparatus, it first passes through a double slit.


5. After that there is some kind of interference detector (SPAD array? Kolenderski, Piotr, et al. "Time-resolved double-slit interference pattern measurement with entangled photons." Scientific reports 4 (2014).). In this case could be a screen Bob will be watching.

Legend

If the affirmation "Entangled photons never show interference in the total pattern without coincidence count" is correct, no interference will be seen by Bob.

Now, if Alice between the steps 3 and 4 (the ideal time would be as the photons get very close to 4, right before the double slit as expected from their synchronized clocks and known distance), measures the polarisation of her photons, the entanglement is broken before Bob's photons arrive at the double slit at step 4.

Thus the photon will have a known polarisation, but that does not interfere with it presenting the typical interference pattern as a non-entagled polarised photon should. Alice is able to choose whether Bob will see the interference pattern or not, nonlocally.

Now to clear up my last question's gedankenexperiment, I also made a drawing for it. The key idea, that circumvents the No-communication theorem, is that once Alice acquires information about the photon's polarisation, she also acquires which-path information. By Wootters, William K., and Wojciech H. Zurek. "Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle." Physical Review D 19.2 (1979): 473., the interference pattern should not show up, even after Bob's attempt to erase which-path information from the system.

This doesn't contradict the No-communication theorem, but allows FTL communication.

It has the same assumptions as the previous gedankenexperiment.

The experiment is:

1. Alice generates a lot of entangled photons (10k for example), sends 1 photon of each pair to Bob and keeps the other photon to herself.


2. Alice keeps her photons undisturbed in some way, could be a mirror in the middle of the path towards Bob. In the diagram I represented it as a "looping device"...


3. Bob's photons take their time to reach Bob's apparatus


4. When the light reaches Bob's apparatus, it first passes through a double slit.


5. After the double slit, comes the which-path markers, in this case horizontal and vertical polarisers for each slit.



6. After the which-path markers, comes the eraser, in this case a 45o polariser.


7. After the eraser, there is some kind of interference detector (SPAD array? Kolenderski, Piotr, et al. "Time-resolved double-slit interference pattern measurement with entangled photons." Scientific reports 4 (2014).). In this case could be a screen Bob will be watching.

Now, if Alice between the steps 5 and 6 measures the polarisation of her photons, she knows which path Bob's photon took (Of the photons Alice measured, 3/4 of photons were twins of photons absorbed along the way and only 1/4 twins of those that hit the interference detector, but that is irrelevant, the point is of all those that hit the screen, Alice knows the which path information). By complementarity, there should not be an interference pattern.

Alice can choose whether to measure the polarisation of her photons in that specific time the experiment is in between steps 5 and 6, controlling whether the interference pattern will show up for Bob or not, nonlocally.

PS.:

• The 10k number of photons is irrelevant, Alice could send them 1 by 1 and Bob would sum all the detected positions to see if an interference pattern was appearing or not.



• The 100% bright source is not necessary, error-correction will be needed on a real protocol anyway, but there seems to be discoveries of sources with around 18% brightness which should already be enough to test it. The SAGNAC's sources used by Zeilinger's group have very low brightness and cannot be used for this experiment.