发表机构
E.ON Digital Technology（E.ON数字技术）
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AdS$_3$中引力与Chern-Simons物质的完整性在电荷共轭下保持偶性，取向编码于纠缠谱电荷不对称性，形成体逻辑量子比特，并通过数值解验证相关性质。
AI 中文摘要
三维爱因斯坦引力和Chern-Simons-Higgs物质都允许Chern-Simons描述，但它们的完整性编码了不同的物理。我们证明电荷共轭反转涡旋缠绕数$n\to-n$，同时逐点保持度规和引力联络不变，因此每个闭合引力完整性特征、BTZ电荷、Bañados数据和领先的几何混合态层级在$n$上严格为偶。在填充相同变量变换的固定标记欧几里得复制品上，$Z_q[n;\mathcal J_+]=Z_q[-n;\mathcal J_+]$，因此不带电的Rényi层级、Faulkner-Lewkowycz-Maldacena单圈修正、重整化广义熵和量子极值曲面在两种取向上重合。互补扇区被精确固定：具有与纠缠区域电荷共轭的Aharonov-Bohm角$\mu$，$Z_q[n;\mu]=Z_q[-n;-\mu]$，因此对称分辨谱满足$\mathcal Z_q(\mathcal Q;n)=\mathcal Z_q(-\mathcal Q;-n)$，每个奇次带电累积量随缠绕数反转。因此，取向完全存储在纠缠谱的电荷不对称性中，并通过链接的带电物质线在拓扑序上读取。该对是体逻辑量子比特，中性引力复制代数在其上作为恒等式的倍数作用。精确BTZ截面表明纯化平台和纠缠楔断开转变是取向盲的，后者以截止无关的跳跃$(c/3)\log(1+\sqrt2)$闭合。数值Bogomolny解验证了奇通量和偶能量与自旋；用作线性化电荷匹配数据时，它们给出偶渐近位移$\delta\widehat M=16\pi Gv^2|n|$和$|\delta\widehat j|=16\pi Gv^2n^2/(mL)$，并有条件地给出有限连续缠绕包络。
英文摘要
Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding $n\to-n$ while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in $n$. On a fixed marked Euclidean replica filling the same change of variables gives $Z_q[n;\mathcal J_+]=Z_q[-n;\mathcal J_+]$, so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle $μ$ conjugate to the entangling-region charge, $Z_q[n;μ]=Z_q[-n;-μ]$, so the symmetry-resolved spectrum obeys $\mathcal Z_q(\mathcal Q;n)=\mathcal Z_q(-\mathcal Q;-n)$ and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump $(c/3)\log(1+\sqrt2)$. Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts $δ\widehat M=16πGv^2|n|$ and $|δ\widehat j|=16πGv^2n^2/(mL)$ and, conditionally, a finite continuous winding envelope.
Comments44 pages, 4 figures
