Just wanted to check if my understanding is correct. So, it is not important who makes the measurement first of the entangled pair, Bob and Alice decohere the particle with each other independently, creating a "spectrum" or Alices and Bobs on each side. This is trivial, local and there are no surprises. Without any communication between Alice and Bob, the sets of Alices and Bobs appears to be independent, however, when they communicate they decohere into pairs where some extra correlation reveals. Is this sketch correct?