aiqbench analysis
This paper investigates the operational consequences of treating a real flag in quotient-space quantum mechanics as an accessible degree of freedom rather than a protected gauge artifact. The authors demonstrate that such accessibility directly violates overlap-determinability and standard no-go theorems, enabling capabilities like probabilistic cloning and steering-based signaling that lie outside the standard complex quantum framework. Ultimately, the work clarifies that real formulations remain equivalent to standard theory only if the underlying complex structure remains hidden, preserving fundamental quantum operational limits.
Phase-Flag Access and No-Go Constraints on Quotient-Space Real Quantum Mechanics
arXiv:2609.20226v1 Announce Type: new Abstract: Barrios Hita et al. [Phys. Rev. Lett. 136, 240202 (2026)] proposed a quotient-space formulation of quantum mechanics over the real numbers and concluded that complex numbers are only a convenience. A preceding analysis [arXiv:2607.05865] showed that, when the construction is empirically equivalent to complex quantum mechanics, its real flag is protected by a hidden complex structure $\hat{J}$ and its composition rule is the balanced tensor product over that structure. Here we ask what would follow from the stronger operational reading that the flag is an accessible real degree of freedom. The answer is a direct clash with overlap-determinability (OD), introduced in [arXiv:2601.14638], and with standard no-go theorems. A readable or coherently controllable flag fixes a representative of each ray, and hence supplies precisely the phase convention that OD identifies as the missing resource for universal superposition of unknown states. Once promoted to a generic phase-access primitive, this resource enables probabilistic cloning of a linearly dependent set, steering-based signaling, and logarithmic-query unstructured search. Thus the quotient construction has a sharp follow-up interpretation: as a protected gauge representation it is standard complex quantum mechanics in real notation; as an accessible real theory it leaves the quantum operational framework.
Abstract:Barrios Hita et al. [Phys. Rev. Lett. 136, 240202 (2026)] proposed a quotient-space formulation of quantum mechanics over the real numbers and concluded that complex numbers are only a convenience. A preceding analysis [arXiv:2607.05865] showed that, when the construction is empirically equivalent to complex quantum mechanics, its real flag is protected by a hidden complex structure $\hat{J}$ and its composition rule is the balanced tensor product over that structure. Here we ask what would follow from the stronger operational reading that the flag is an accessible real degree of freedom. The answer is a direct clash with overlap-determinability (OD), introduced in [arXiv:2601.14638], and with standard no-go theorems. A readable or coherently controllable flag fixes a representative of each ray, and hence supplies precisely the phase convention that OD identifies as the missing resource for universal superposition of unknown states. Once promoted to a generic phase-access primitive, this resource enables probabilistic cloning of a linearly dependent set, steering-based signaling, and logarithmic-query unstructured search. Thus the quotient construction has a sharp follow-up interpretation: as a protected gauge representation it is standard complex quantum mechanics in real notation; as an accessible real theory it leaves the quantum operational framework.
This work is a follow-up to our previous study, arXiv:2607.05865
arXiv:2609.20226 [quant-ph]
(or arXiv:2609.20226v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.20226 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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