$\newcommand{\ket}[1]{|#1\rangle}$ My question is a follow-up from this discussion about the presence of non-local correlations in a theory that is deemed local. The first answer talks about the inability to use entaglement for superluminal communication between oberservers. This explanation also came up in an answer to another question that is closely related to mine. I had to prove this concept as part of my curriculum and understood the idea with the help of a specific example. The argument could be condensed as follows:
Two observers, Alice and Bob, are allowed to decide the bases in which they would conduct measurements before they and their respective qubits are separated in space by some arbitrary amount. For the sake of generality, we assumed that Bob chose a basis expressed as $\vec{n}(\theta, \phi).\vec{\sigma}$ in the matrix form (I am denoting the corresponding basis vectors as $\ket{\theta, \phi}^+$ and $\ket{\theta, \phi}^-$). In this particular example, they had a $\ket{\Phi^+}$ bell state as the shared qudit. The exercise was to find out if Alice could choose a basis such that Bob's qubit would always be in one of his basis states after her measurement. It was found possible, if Alice performed her measurements in the $\vec{n}(\theta, -\phi).\vec{\sigma}$ basis (basis vectors: $\ket{\theta, -\phi}^+$ and $\ket{\theta, -\phi}^-$). However, for any measurement performed by Alice, the probability that Bob would obtain $\ket{\theta, \phi}^+$ or $\ket{\theta, \phi}^-$ after his measurement would always be half and half. This implied that there is no measurement that Alice could perform to make Bob's measurement results 'meaningful' (contain any non-trivial information).
Through this example, I understand why information in the form of bits or bit strings could not be communicated instantaneously using entanglement. However, the information about the occurance of a measurement still seems to be happening instantaneously. In other words, considering the Copenhagen interpretation, the information that Bob's qubit needs to 'collapse' after Alice's measurement still seems to be getting transferred instantaneously. My notion of locality is that it should be related more to the fundamental information about the occurance of events (measurements in this case) than to the information contained in bit strings.
Parallelly, one could argue that the 'collapse' itself should not be treated within the framework of physics, since the two superposed states represent two alternate realities. Would this idea be reminiscent of the many-worlds interpretation? If we were to resort to that interpretation, it could actually resolve this issue because, according to my (probably naive) understanding, we could say that "the correlations kind of always existed retrocausally" after diverging into a particular 'branch' formed by a measurement. There would be no reason to appeal to hidden variables or non-locality to explain the correlations in that case. Does this not make the Copenhangen and many world interpretations distinguishable? And does it not give more credibility to the latter? Also, as a slightly tangential question, is retrocausality always associated with the many-worlds interpretation, or could it also be compatible with other interpretations?
