[akvadrako]

There is lots of mathematical evidence that every quantum state maps 1-to-1 on a physical state¹, or at least be uniquely determined by the physical state². The main assumption both make is that there is some physical state.

So it doesn't really matter if it's a map or not - it tells you something about the territory.

[1] The completeness of quantum theory for predicting measurement outcomes, https://arxiv.org/abs/1208.4123

[2] On the reality of the quantum state, https://arxiv.org/abs/1111.3328v3

[n4r9]

> The main assumption both make is that there is some physical state.

I'd phrase this as: the main assumption is that reality is literally encoded by some sort of objective hidden variables theory.

[akvadrako]

I'm not sure what your point is, but it doesn't have to be hidden and in this case, objective just means two parties agree on the outcomes of experiments.