AI 中文总结
该研究将量子置换引入物理学，推广了量子参考系，揭示量子场非对易性对应真正量子置换，通过多示例展示其特性，形式体系有望应用于量子引力及量子信息领域。
AI 中文摘要
量子置换（又称魔法幺正）近年来已被用于识别图的“真正量子”等距映射的研究中。本文将该工具引入物理学领域，证明量子置换可在离散场景下推广量子参考系，其推广方式类似于从狭义相对论到广义相对论的过渡。我们表明，典型的量子参考系框架对应于数学文献中被归类为“经典”的量子置换，且我们证明这类置换是量子受控变换（经典坐标映射的叠加）。真正的量子置换具有两个核心特性：（i）可构造“非对易”的量子参考系；（ii）对应变换的“局域”叠加，而非全局叠加。值得注意的是，我们发现量子场的非对易性（当用作参考系统时）恰好意味着参考系的变换需通过真正的量子置换实现。我们用第一和第二量子化形式的多个示例说明上述结论，这些示例展示了：（a）对非对易变量的同时控制；（b）存在可通过真正量子置换局域化、而无法通过常规量子参考系变换（不引入额外自由度）局域化的 bipartite 态；（c）将伊辛模型对称性扩展至真正量子置换；（d）将弯曲时空中标量场作用量的对称性扩展至真正量子置换。尽管我们的研究着眼于量子引力领域的应用，但预计该形式体系也将在量子信息的广泛主题中受到关注。
英文摘要
Quantum permutations, or magic unitaries, have in recent years been explored in the context of identifying `genuinely quantum' isometries of graphs. Here, we import this tool in physics, showing that quantum permutations yield a generalisation of quantum reference frames in a discrete setting that is reminiscent of the passage from special to general relativity. We show that the typical quantum reference frames framework corresponds to quantum permutations classified as `classical' in the mathematical literature, and which we demonstrate are quantum controlled transformations (superpositions of classical coordinate maps). Genuinely quantum permutations (i) allow to construct \emph{non--commuting} quantum reference frames (ii) correspond to \emph{local}, as opposed to global, superpositions of transformations. Strikingly, we find that the non-commutativity of quantum fields, when used as reference systems, is exactly what implies that the change of frame is achieved through a genuine quantum permutation. We illustrate the above with several examples in both first and second quantization formalism, which demonstrate (a) simultaneous control on non--commuting variables, (b) the existence of bipartite states that can be localized with a genuine quantum permutation and cannot be localized with the usual quantum reference frame transformations (without introducing additional degrees of freedom), (c) extension of the Ising model symmetries to genuinely quantum permutations, and (d) extension of the symmetries of a scalar field action on curved spacetime to genuinely quantum permutations. While we have in mind applications in quantum gravity, we expect our formalism to be of interest in a wide range of topics in quantum information.
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