Dear Del Santo and Cardelli,
Your paper is very well written. Your focus on no-go theorems with respect to quantum mechanics is a good overview of that area. It is as you indicate the case that modern physics does lean on such ideas. In relativity there is something similar with the invariance of the interval that gives a "no-go" theorem result that information and matter must move at the speed of light or slower.
These bounds on quantum mechanics and no-go theorems such as no-signaling and no-cloning have interesting analogues with spacetime. For instance we have the no-cloning theorem that a quantum state |П€> can't be cloned in a unitary transformation |П€> в†' |П€>|П€>. This can be seen if we write this quantum state as |П€> = a|1> + b|2> so this cloning is
|П€>|П€> = a^2|1>|1> + b^2|2>|2> + ab(|1>|2> + |2>|1>),
but cloning on the basis {|1>, |2>}gives
|П€>|П€> = a^2|1>|1> + b^2|2>|2>.
This means cloning is basis dependent, which violates unitarity. This connects with spacetime physics if we assume we have a spacetime has a wormhole. A wormhole where one opening is transformed under a succession of Lorentz boosts or a send and return motion will exhibit closed timelike curves. It would then be possible to clone a quantum state. An observer with the quantum state |П€> will have a copy appear so that |П€> в†' |П€>|П€> if that observer later throws one |П€> into the wormhole.
The types of spacetime solutions that may exist could then be constrained by quantum no-go theorems and restrictions on quantum measurements. I wrote a paper last year on a correspondence between the Tsirelson bound and the invariant interval of spacetime and how spacetime is built from entanglements. In general we then have that spacetime physics and quantum mechanics are mirrors of each other. The limits in both of these areas are then specific manifestations of the same constraints. It could be that the ultimate foundations of physics is just plain vanilla quantum mechanics.
I wrote an essay that attempts to look at this correlation between quantum mechanics and general relativity. In part I attempt to look at empirical ways of supporting or falsifying this. At any rate I enjoyed your essay
Cheers LC