Entanglement, classical correlation, and questions about superluminal signalling

[Physics Monkey]

The quantum physics forum is full of questions about why entanglement can't be used to signal superluminally.

My question is this: do these questions usually still make sense if we replace entanglement by classical correlation? For example, I can send Alice and Bob each a random bit but with both bits perfectly correlated. At the level of the typical entanglement/superluminal signaling question, are these any different e.g. since Alice has the same (completely mixed) state in both case? I realize this is a bit soft, so your opinions and impressions are very welcome. Basically what I want to know is if people are really asking about entanglement or merely any kind of correlation.

And let me clear, I am certainly very aware that entanglement is not the same as classical correlation, and of Bell's theorem, and so on. In my mind, this question is really about the very basic issues and about pedagogy.

 

[martinbn]

I probably didn't understand your question, but if there is no entanglement i.e. if the state is separable, then isn't 'obvious' that there cannot be superluminal signaling?

 

[Demystifier]

I would reformulate the Physics Monkey's question in the following way. Assume that Alice is correlated with Bob through a superluminal signal sent from Alice to Bob. Assume further that this signal is chosen randomly, i.e., not freely chosen by Alice. The questions is: Can Alice use it to send a USEFUL signal to Bob? The answer is no, because random signals are not useful.

 

[Physics Monkey]

I probably didn't understand your question, but if there is no entanglement i.e. if the state is separable, then isn't 'obvious' that there cannot be superluminal signaling?

Perhaps so, and this is sort of what I was trying to get at. Most of the questions I've seen seem to be using nothing more than the fact that outcomes are correlated (plus the spooky language of particles deciding what to do based on their distant counterpart's measured state) as some of kind of suggestion of superluminal signaling.

The state I described is separable but still correlated: $\rho = \frac{1}{2} |\uparrow \rangle \langle \uparrow |_A |\uparrow \rangle \langle \uparrow |_B + \frac{1}{2}|\downarrow \rangle \langle \downarrow |_A |\downarrow \rangle \langle \downarrow |_B$. My feeling is that these sorts of questions aren't using anything more than the correlation displayed here.

What I'm trying to do is understand whence these questions about entanglement originate. Is it a bad metaphor we're using?

 

[Physics Monkey]

I would reformulate the Physics Monkey's question in the following way. Assume that Alice is correlated with Bob through a superluminal signal sent from Alice to Bob. Assume further that this signal is chosen randomly, i.e., not freely chosen by Alice. The questions is: Can Alice use it to send a USEFUL signal to Bob? The answer is no, because random signals are not useful.

This is an interesting reformulation. At the level of comparing correlated outcomes, one could imagine that Alice measuring the state of her spin really does set the state of Bob's spin via superluminal signal. But its not clear to me what the state of Bob's (classical?) spin is before Alice's measurement. It is probably also important that this superluminal state resetting can only happen once and that Bob can't actually determine when it happened.