Comment on "Quantum theory based on real numbers cannot be experimentally falsified": On the compatibility of physical principles with information theory for fermions

Abstract

The manuscript [arXiv:2603.19208] proposes a physically motivated postulate to select the appropriate formulation of quantum theory over real Hilbert spaces, ruling out the theory considered in [Nature 600, 625-629 (2021)] in favour of the alternative theory which reproduces the predictions of standard quantum information theory (QIT). Here, we first make the claim that a general physical postulate should in particular be satisfied by Fermionic Information Theory (FIT), the standard framework describing information encoded in the presence or absence of identical fermions. We then show that this postulate proposed by [arXiv:2603.19208] fails in FIT, hence is not a general physical postulate according to our claim. More broadly, our results highlight the importance of confronting proposed foundational principles with fermionic information theories, a point that also deserves further examination in recent related works such as [arXiv:2503.17307] and [arXiv:2504.02808].