What is Fundamentally Quantum?

What makes quantum mechanics so strange, and so different from quantum mechanics?

Here is a common opinion:

Following the EPR paper, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word Verschränkung (translated by himself as entanglement) "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."[19] However, Schrödinger had discussed the phenomenon as early as 1932.[20]

Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated:[3] "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."

Sometimes indeterminacy or other features are said to be fundamentally quantum.

I believe this is mistaken. I have said so many times on this blog, such as here. The only thing that fundamentally distinguishes quantum from classical mechainis is the noncommutation of observables.

Flavio Del Santo, Nicolas Gisin write a new paper:P

What is fundamentally quantum? We argue that most of the features, problems, and paradoxes -- such as the measurement problem, the Wigner's friend paradox and its proposed solutions, single particle nonlocality, and no-cloning -- allegedly attributed to quantum physics have a clear classical analogue if one is to interpret classical physics as fundamentally indeterministic. What really characterizes quantum physics boils down only to phenomena that involve $\hbar$, i.e., incompatible observables.

I agree with this. Classical mechanics is not really deterministic, if you take into account the fact that the variables can only be known to finite precision. Then classical and quantum mechanics are similarly indeterministic.

THe commutator of position and momentum is ℏ, ie h-bar, Planck's constant. That is the core of the uncentainty principle and everything that is truly quantum. There is no other fundamental quantum mystery.

The authors even point out that many-worlds theory can just as easily be applied to a classical theory. Just assume that all possibilities are real. It also says that there is a classical no-cloning theorem. I will have to think about that one.