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

Quantum Physics [Submitted on 8 Apr 2026] Comment on "Quantum theory based on real numbers cannot be experimentally falsified": On the compatibility of physical principles with information theory for fermions Fatemeh Moradi Kalarde, Xiangling Xu, Marc-Olivier Renou 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]. Comments: Comment on arXiv:2603.19208. 5+5 pages. Feel free to discuss Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.07425 [quant-ph]   (or arXiv:2604.07425v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.07425 Focus to learn more Submission history From: Fatemeh Moradi Kalarde [view email] [v1] Wed, 8 Apr 2026 17:10:22 UTC (13 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)