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

TL;DR

This paper critiques a proposed postulate for quantum theory, demonstrating it does not hold in Fermionic Information Theory, emphasizing the need to test foundational principles against fermionic frameworks.

Contribution

It shows that a recent physical postulate fails in Fermionic Information Theory, challenging its universality and highlighting the importance of fermionic considerations in foundational physics.

Findings

The proposed postulate does not apply to Fermionic Information Theory.

Fermionic frameworks must be considered when testing foundational quantum principles.

The critique encourages broader examination of principles in fermionic contexts.

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].