发表机构
Università degli Studi di Palermo; Université Paris Cité and Université de La Réunion（巴勒莫大学; 巴黎西岱大学和留尼汪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明扇形闭包可消除理论与对称化子理论的关联间隙，指出限制效应能隐藏因果结构中的非物理对称性，为量子理论的对称性边界问题提供了有限计算方法。
AI 中文摘要
实振幅量子理论是量子理论在复共轭下不变的子理论，而独立源网络中的实验已测量到超过实界的关联。然而，某一理论即便不具备完全正定性，仍可携带相同的复共轭对称性，且在包括双局域场景在内的任意因果结构中，其关联恰好等于自身共轭不变子理论的关联。该理论的所有态均为密度矩阵，其效应是所有部分转置后仍为量子效应的算符。当每个源携带参考帧而非每个系统时，该理论的对称化子理论会模拟它。因此，某一映射在三个理论中会得到三种不同判定，故仅对称性无法标记边界，维持量子理论分离性的是量子理论的特有属性。量子理论允许其态所允许的所有效应，而该理论不具备此特性。存在边界的是理论与其对称化子理论的关联一致的理论类。我们证明，扇形闭包（即效应和操作在对称性独立作用于每个源下的不变性）对任意有限群而言，足以消除间隙，且无法在效应层面弱化。固定无限制态和复共轭会使该理论的效应成为对称性允许的最大效应，操作成为最大的扇形闭包操作。对于由固定 bound 纠缠态构建的候选效应集，定位扇形闭包失效的位置是对单个效应射线的有限计算。
英文摘要
Real-amplitude quantum theory is the subtheory of quantum theory invariant under complex conjugation, and experiments in networks of independent sources have measured correlations above the real bound. We construct a theory on which the same conjugation fails complete positivity and still leaves every probability in the unit interval, and whose correlations are exactly those of its own conjugation-invariant subtheory in every causal structure, the bilocality scenario included. Its states are all the density matrices, its effects are the operators every partial transpose of which is again a quantum effect, and its operations are the completely PPT-preserving maps. The symmetrized subtheory simulates it once each source carries a reference frame rather than each system. One map therefore receives three different verdicts in three theories, so the symmetry alone marks no boundary at all. Quantum theory admits every effect its states permit, and no theory with that property can hide a symmetry this way, so what sustains the separation measured in the network experiments is the absence of a restriction rather than any feature of conjugation. What does have a boundary is the class of theories whose correlations coincide with those of their symmetrized subtheory. We show that sectorial closure, meaning invariance of the effects and the operations under the symmetry acting independently on each source, suffices for the absence of a gap under any finite group, and that it cannot be weakened on the effects. Fixing unrestricted states and conjugation makes the effects of this theory the largest the symmetry admits and its operations the largest sectorially closed ones, so it is not one construction among several. Locating where sectorial closure fails, for a candidate effect set built from a fixed bound entangled state, is a finite computation on a single ray of effects.
Comments35 pages, 1 figure, 2 tables. Ancillary files contain the verification script and the certificate, also deposited at https://doi.org/10.5281/zenodo.22648589
