I was skeptical about a new paper on the reality of the quantum wave function, because it claims to disprove the probabilistic interpretation of quantum mechanics.
Part of the confusion is that the title of the new paper is "The quantum state cannot be interpreted statistically". That is misleading, as it is certainly possible to interpret the quantum wave function statistically. What the paper argues is that the wave function cannot be just a probability distribution for hidden variables.
The paper has generated a lot of attention, and another new paper explains it and gives a similar result. It is Completeness of quantum theory implies that wave functions are physical properties.
Here is the issue. By 1926, it was clear that Heisenberg uncertainties were essential to quantum mechanics. Von Neumann's 1932 textbook considered the possibility that the uncertainties could be eliminated by a hidden variable theory, and argued that no such theory was possible. Hidden variables are physical characteristics, like position, momentum, or spin, which determine the nature of a something, but which are not directly observable. Einstein coauthored a 1935 paper arguing for such a theory anyway.
You can think of an electron wave function as telling you the probability that the electron will be found in a particular region. But if you think of the electron as a point particle, and the wave function as just a probability distribution for the position of that point particle, then you will run into trouble because Heisenberg uncertainty says that the electron cannot be a point particle.
While a lot of work has gone into this issue, most physicists consider the Bell test experiments to be the definitive proof that the hidden variable theories are impossible.
These new papers are additional arguments against hidden variables. They confirm what everyone since 1932 has believed, except for a few curmudgeons like Einstein.