The proposed postulate for choosing between real-number versions of quantum theory does not hold in Fermionic Information Theory and therefore is not general.
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
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Comment on "Quantum theory based on real numbers cannot be experimentally falsified": On the compatibility of physical principles with information theory for fermions
The proposed postulate for choosing between real-number versions of quantum theory does not hold in Fermionic Information Theory and therefore is not general.