I have read in many places that apparent faster-than-light transmission of information is made possible by quantum entanglement as measurements of an entangled system will always be random.
I recently came across this article which discusses (as I understand it) how in an experiment two particles 1 and 4 became entangled with each other by entangling particle 1 with another particle 2 and particle 4 with particle 3 and then finally entangling particles 2 and 3 with each other.
This got me wondering about the possibility of a larger experiment which involves $2n$ particles (where $n$ is large), where the one half of $n$ particles have been pairwise entangled to particles from the other half.
Say person-1 who is standing with one half of the particles, decided to entangle all their particles. Would this have the effect of entangling person 2’s $n$ other particles with each other simultaneously and if so, couldn’t this be used to send a message from one place to another faster than the speed of light? The idea being that person 2 could notice how measurements of one of their particles was correlated with measurements of another. If $n$ is a large number this is unlikely to happen by chance, thus he could conclude that their particles had become entangled