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 an alternative theory which reproduces the predictions of standard complex quantum information theory. Here, we argue that, to qualify as a general physical principle, this postulate should also hold in fermionic quantum information theory, the standard framework describing information encoded in the presence or absence of identical fermions. We show, however, that it fails in this framework. More broadly, our result highlights the importance of confronting proposed foundational principles with fermionic quantum information theory, a point that also deserves further examination in recent related works such as [arXiv:2503.17307] and [arXiv:2504.02808].

Comment on arXiv:2603.19208. 7+5 pages. v2: Revised presentation and clarified terminology; main results unchanged

arXiv:2604.07425 [quant-ph]

(or arXiv:2604.07425v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.07425 Focus to learn more arXiv-issued DOI via DataCite

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