Here's another write-up of the same subject: https://arstechnica.com/science/2018/09/quantum-observers-wi...
"Quantum observers with knowledge of quantum mechanics break reality"
"Quantum observers with knowledge of quantum mechanics break reality"
In one of the outcomes authors examine, which gives the rise to the apparent contradiction, measurements do no commute, which means, according to QM it is impossible to get that set of results in real world.
The authors' final response to referee #2:
We thank the referee for the clarification of their earlier comment, which we indeed misunderstood. It is of course correct that the observable of the measurement leading to z does not commute with the one corresponding to the measurement of w . This also means that the values z and w cannot be defined simultaneously (in the sense of “at the same time”). To explain how our argument avoids this problem, note first that the measurements take place at different times (as pointed out in the reply above). Concretely, z is measured at time n :10 and w is measured at time n :30. Note also that, in all statements we are using, we always explicitly specify the time at which a variable is supposed to have a given value. Whenever we are talking about z , the corresponding time lies (strictly) before n :30, whereas we only talk about what value w has at times after n :30. We hence never need to assume that z and w are available at the same time. To clarify this in the manuscript, we have changed the labelling of all statements. They now have a superscript which indicates at what time a statement has been made by an agent.
Plainly speaking, this argument does not make sense, because there's no such thing as simultaneity.
The way I see it, the commuting argument tells what you, an observer to the entire system, can or can not see at some fixed point in spacetime, that is casually descended from the points where observations occur.
Anyway, the whole discussion about validity of interpretations does not make any sense to me, as long as they represent the same underlying math.
In particular, in the iterative process, that authors suggested to use to get w=ok, z=ok, each iteration must be connected to the previous in some QM encodable way, eg as { |continue>, |halt> }, that must be set in the last step, and measured in the first, therefore combining all participants into a single entangled QM system.
It is not immediately obvious, that this addition would not affect the outcome of experiment, and hence should at very least be included in the paper.