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Since complex numbers are isomorphic to a real 2x2 matrix algebra, I was confused how such a claim can be made. I tried several times to find the PF threads on this with no success. A relevant peer review reference is, Phys Rev Let 129, 140401, (2022).

Reading only the introduction of the letter, it appears there are measurable consequences in how composite systems are formed by tensor products of real versus complex Hilbert spaces. Anyway, if there are PF discussions, a link would be appreciated. If not any comments would be.