相位标志访问与商空间实量子力学的禁戒约束
Phase-Flag Access and No-Go Constraints on Quotient-Space Real Quantum Mechanics
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中文总结 AI 辅助
本文分析商空间实量子力学中标志可访问性的后果，表明其与重叠可判定性及禁戒定理冲突，并指出该资源可实现概率克隆、导引信号传递和对数查询搜索，从而明确其规范表示与可访问理论的双重解读。
中文摘要 AI 辅助
Barrios Hita等人[Phys. Rev. Lett. 136, 240202 (2026)]提出了实数域上量子力学的商空间表述，并得出结论：复数仅是一种便利。先前的一项分析[arXiv:2607.05865]表明，当该构造在经验上等价于复量子力学时，其实数标志受到隐藏复结构$\hat{J}$的保护，其合成规则是该结构上的平衡张量积。在此，我们探讨若采纳更强的操作性解读——即该标志是一个可访问的实数自由度——将会产生何种后果。答案是它与重叠可判定性(OD)（引入于[arXiv:2601.14638]）以及标准禁戒定理直接冲突。一个可读或可相干控制的标志固定了每条射线的代表元，从而恰好提供了OD所认定的、实现未知态通用叠加所缺失的相位约定资源。一旦提升为通用的相位访问原语，该资源即可实现线性相关集的概率克隆、基于导引的信号传递以及对数查询非结构化搜索。因此，商构造具有一个明确的后续解读：作为受保护的规范表示，它是实数记号下的标准复量子力学；作为可访问的实数理论，它则脱离了量子操作框架。
英文摘要
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.
发表机构
- Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。
