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arxiv: 2604.07425 · v1 · submitted 2026-04-08 · 🪐 quant-ph

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 This is my paper

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification 🪐 quant-ph
keywords fermionic information theoryquantum foundationsreal quantum theoryphysical postulatesindistinguishable particlesquantum informationcomplex Hilbert spaces
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The pith

A proposed postulate to select complex quantum theory over real versions fails to hold in the standard theory for identical fermions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that any truly general physical postulate must hold in Fermionic Information Theory, the standard framework for information carried by identical fermions. It examines a recent postulate intended to favor the complex Hilbert space formulation of quantum theory that matches ordinary predictions over a real-number alternative. The authors demonstrate that the postulate is violated within this fermionic setting. As a result, the postulate cannot qualify as a universal physical principle under the stated criterion. The work calls for testing other foundational proposals against fermionic information theories as well.

Core claim

We first make the claim that a general physical postulate should in particular be satisfied by Fermionic Information Theory (FIT). 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.

What carries the argument

The compatibility test of a proposed physical postulate against Fermionic Information Theory (FIT), the standard framework for information encoded in the presence or absence of identical fermions.

If this is right

  • The examined postulate is not general because it is not satisfied by FIT.
  • Any candidate foundational principle must be checked for consistency with the standard description of information for identical fermions.
  • Similar compatibility tests are required for other recent proposals on quantum foundations such as those in arXiv:2503.17307 and arXiv:2504.02808.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Principles formulated without reference to particle indistinguishability may apply only to distinguishable systems.
  • A revised version of the postulate could be sought that remains valid when extended to fermionic statistics.
  • Systems of identical particles offer an independent arena for probing whether real-number formulations of quantum theory remain viable.

Load-bearing premise

Any general physical postulate must necessarily be satisfied by the standard Fermionic Information Theory framework describing information in identical fermions.

What would settle it

An explicit calculation or example showing that the proposed postulate holds for at least one fermionic configuration or state would demonstrate that it does not fail in FIT.

read the original 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].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. This manuscript is a comment on arXiv:2603.19208. It asserts that any general physical postulate must be satisfied by Fermionic Information Theory (FIT), the standard framework for information in identical fermions. The authors then claim to exhibit a failure of the postulate from arXiv:2603.19208 inside FIT, concluding that the postulate is therefore not general. The paper also recommends that related works (arXiv:2503.17307 and arXiv:2504.02808) be examined in light of fermionic information theories.

Significance. If the failure of the postulate inside FIT can be shown rigorously and the scope extension is justified, the result would indicate that the postulate lacks the generality claimed in arXiv:2603.19208 and would usefully highlight the need to test foundational principles against fermionic Fock-space settings. The manuscript earns credit for explicitly raising the compatibility of physical postulates with fermionic information theory, an aspect that has received limited attention in recent related literature.

major comments (2)
  1. [Abstract (paragraph beginning 'We first make the claim...')] The central claim that a general physical postulate must in particular be satisfied by standard Fermionic Information Theory is asserted without derivation or justification. The original postulate is motivated inside standard QIT with fixed-particle or bosonic considerations; no argument is supplied showing why it is required to hold unchanged in the variable-particle-number fermionic Fock-space setting.
  2. [Abstract (paragraph beginning 'We then show that this postulate...')] The demonstration that the postulate fails in FIT is stated but not accompanied by the explicit mapping of the postulate into FIT or the concrete counterexample. Without this derivation, it remains unclear whether the reported failure is a direct contradiction or an artifact of how the postulate is re-expressed in the fermionic formalism.
minor comments (1)
  1. The relevance of the cited works arXiv:2503.17307 and arXiv:2504.02808 to the present argument could be stated more explicitly in one sentence.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting areas where the manuscript could be clarified. We address the two major comments below. Both can be resolved by adding explicit justification and a more detailed derivation in the revised version, without altering the core argument.

read point-by-point responses

  1. Referee: [Abstract (paragraph beginning 'We first make the claim...')] The central claim that a general physical postulate must in particular be satisfied by standard Fermionic Information Theory is asserted without derivation or justification. The original postulate is motivated inside standard QIT with fixed-particle or bosonic considerations; no argument is supplied showing why it is required to hold unchanged in the variable-particle-number fermionic Fock-space setting.

    Authors: We agree that the manuscript would benefit from an explicit justification for why a physically motivated postulate should apply to FIT. Our reasoning is that any claim of physical generality for a foundational principle in quantum theory must extend beyond the fixed-particle or bosonic sectors of standard QIT to include the variable-particle-number fermionic Fock space, which is the natural setting for identical fermions. FIT is the established framework for information-theoretic tasks in this regime, and the absence of the postulate's validity there undermines its generality. We will insert a concise paragraph in the introduction deriving this expectation from the requirement that physical postulates be independent of the specific particle statistics or number sector. revision: yes

  2. Referee: [Abstract (paragraph beginning 'We then show that this postulate...')] The demonstration that the postulate fails in FIT is stated but not accompanied by the explicit mapping of the postulate into FIT or the concrete counterexample. Without this derivation, it remains unclear whether the reported failure is a direct contradiction or an artifact of how the postulate is re-expressed in the fermionic formalism.

    Authors: The full manuscript contains the explicit mapping of the postulate into the fermionic Fock-space formalism together with the concrete counterexample (a specific state and observable set in FIT that violates the postulate while satisfying all other physical requirements). However, we acknowledge that the presentation could be made more self-contained to avoid any ambiguity about whether the failure is direct. In the revision we will add a short dedicated subsection immediately after the abstract that spells out the mapping step by step and reproduces the counterexample in full detail, thereby confirming it is a genuine contradiction rather than a formal artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on explicit claim about generality plus standard FIT definitions, without reduction to self-referential inputs or fitted predictions.

full rationale

The paper states its central premise as an explicit claim ('a general physical postulate should in particular be satisfied by Fermionic Information Theory (FIT)') and then exhibits the failure of the external postulate from arXiv:2603.19208 inside that framework. No step reduces by construction to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain whose content is unverified. The argument uses standard definitions of FIT and an independent external reference, remaining self-contained rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the domain assumption that FIT is the appropriate standard framework any general postulate must satisfy, plus the definitions of the postulate from the commented manuscript. No free parameters or new entities are introduced.

axioms (1)
  • domain assumption A general physical postulate should in particular be satisfied by Fermionic Information Theory (FIT)
    This premise is explicitly stated in the abstract as the basis for concluding the postulate is not general.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

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