Entangled photons polarization

[Tom_]

Hello physicist,

I have a question about the interaction of entangled photons passing throught polarizers. I asked chatGPT but I'm not so sure about the answer, I would feel much safer to ask an expert.

If we have a setup that look like that (circles are polarizers and the lines represent the angle):

We have 2 entangled photons with the same poilarization but going in differents directions (the source is represented by the black rectangle).

The first one pass throught a vertical polarizer at a distance of one meters to the source (or less, that's not important).

The second one pass throught a horizontal polarizer situated at a distance of 1 light year and 10 meters from the source and hit a screen 1 meter farther.

Now, according to chatGPT, if I add a 45 degrees polarizer in the first photon path, at at distance of 1 light year from the source, it should change the probability of the second photon hitting the screen (using multiple photon pairs, it would change the intensity of the light on the screen).

But that's when it become contradictory: Still according to chatGPT, the second photon won't be affected by the act of adding the 45 degree polarizer because there is only 10 meters left to travel while the information that the polarization changed should travel at the C or slower.

It mean that the same setup would produce a light intensity difference on the screen if the horizontal polarizer is 2 light year away (for exemple) from the source but it would take one year (if we consider that the distance between the 45 degree polarizer and the horizontal polarizer is 1 light year).

So which one is true?

Will the second photon pass the horizontal polarizer because the change in his partner polarization should be instantaneous?

Or will the second photon be blocked by the horizontal polarizer because the information that his partner polarization changed did not traveled fast enought to reach it before the horizontal polarizer block it?

I suspect that it won't affect the second photon since we could use the 2 differents light intensity as a bit (1 and 0) and transfer information faster than the speed of light (by adding and removing the 45 degree polarizer, creating a controled signal) but I thought that nonlocality mean that these kind of actions at a distance should be instantaneous. 

Edited August 11, 2023 by Tom_
Typo and word missing

[Genady]

After the first photon passes the vertical polarizer, the photons are not entangled anymore, and there is no further correlation between them regardless of what is done to any of them.

[swansont]

2 hours ago, Tom_ said:

Will the second photon pass the horizontal polarizer because the change in his partner polarization should be instantaneous?

There is no change in the partner polarization. If the photons’ polarizations are entangled, you don’t know either photon’s polarization state, only the correlation.

Measurement of one photon means both photon states are determined.

[Tom_]

That make a lot more sense, thank you!