> They say that if we use two entangled photons and let them fly far apart, then pass one of them through two filters, and the second photon through the middle filter, the first photon will be affected - it will get a chance to pass though the pair of filters.

I don't think that can be correct. This would allow FTL communication of information. I could put the filter in the path of the second photon when I wanted to send a 1 and leave it out of the path of the second photon when I wanted to send a 0. In the 1 case the other side would sometimes see the photon pass both filters. In the 0 case the other side would never see the photon pass both filters. Combine this with a little error correction and you have a channel for transmitting arbitrary information faster than light which would violate the no-communication theorem. https://en.wikipedia.org/wiki/No-communication_theorem

The MinutePhysics video you link describes a different setup with only one filter in the path of each photon. This gives you some information about the probability that other photon got past its filter but it doesn't let you transmit anything.