Recently I presented on the paper by Renou, et. al. in Nature (Quantum theory based on real numbers can be experimentally falsified) developing an experimental technique for rejecting real formulations of quantum mechanics. An important part of the paper was the assumption of local tomography - that states describing multiple degrees of freedom can be fully described by local measurements on each individual degree of freedom. To me, the paper concluded (indirectly) that either we live in a complex universe with local tomography, or the universe is somehow terribly non-local if we choose to describe it in terms of real numbers only. There wasn't a clear differentiation between those two options because the paper didn't address non-local real number theories.
As a first-year grad student working in quantum information, I don't have much exposure to theories that don't necessarily require local tomography, so right now it's hard to wrap my head around them. Path integrals were mostly nuances for people who were concerned about electrons and atoms, and didn't seem too particularly important to my field of interest. But I came across this paper that derives the results of path integral calculations on entangled qubit systems (Spacetime Path Integrals for Entangled States). They show that for a good number of cases (and I'm guessing one can extrapolate to all cases) that interference in entangled qubit systems can be fully modeled by path integrals and arrives at the same conclusion as tensor product calculations. I'll admit, right now I only have time to scan the paper and it's results so there might be something I'm missing here.
Does this mean that it isn't possible to discern between theories requiring local tomography and those that don't? On it's face that seems problematic. Are there certain implications for quantum mechanics if local tomography is shown not to be axiomatic? Is there a greater part of the picture I'm missing here? This is all very confusing and somewhat unsettling to me.
