> As I understand the situation, usually quantum mechanics uses correlation for examples of entanglement where it appears that, yes, the stronger functionally dependent would hold, and, thus, be more appropriate.
Not really, since things can be weakly entangled, and thus measuring one thing doesn't totally determine the other. The kind of entanglement where you have perfect correlation is usually only achievable in certain strange situations, like EPR entanglement. In that case it can be seen as perfect correlation though, which I don't see as being any different from the functional dependence you speak of.
In most cases in quantum systems, we have some correlation but not perfect correlation (e.g. squeezed states of light), and since we have that whole spectrum of behaviour, with maximum entanglement (e.g. some kind of EPR) being the extreme, we choose to use correlation to quantify the entire spectrum of possibilities.
Also from a more philosophical point of view, we expect to treat different degrees of freedom separately. If you have two particles but measuring the momentum of one gives you perfect knowledge of the other (i.e. EPR), it still doesn't really make sense to say p' = -p, or whatever, since conceptually p' and p are momenta belonging to two different subsystems. The most neutral way of stating it is that the momenta are perfectly correlated.
Not really, since things can be weakly entangled, and thus measuring one thing doesn't totally determine the other. The kind of entanglement where you have perfect correlation is usually only achievable in certain strange situations, like EPR entanglement. In that case it can be seen as perfect correlation though, which I don't see as being any different from the functional dependence you speak of.
In most cases in quantum systems, we have some correlation but not perfect correlation (e.g. squeezed states of light), and since we have that whole spectrum of behaviour, with maximum entanglement (e.g. some kind of EPR) being the extreme, we choose to use correlation to quantify the entire spectrum of possibilities.
Also from a more philosophical point of view, we expect to treat different degrees of freedom separately. If you have two particles but measuring the momentum of one gives you perfect knowledge of the other (i.e. EPR), it still doesn't really make sense to say p' = -p, or whatever, since conceptually p' and p are momenta belonging to two different subsystems. The most neutral way of stating it is that the momenta are perfectly correlated.