AI 中文总结
本研究在全息CFT框架下，探究部分纠缠热态约化密度矩阵的稳定子复杂度，发现bulk几何存在Python午餐时其维格纳负性及稳定子复杂度呈指数级增强。
AI 中文摘要
在本注记中，我们研究了全息CFT中具有固定能量边界条件的部分纠缠热（PET）态一侧对应的约化密度矩阵的稳定子复杂度。特别地，我们研究了维格纳负性（Wigner negativity），这是一种具有操作意义的魔法单调量，可解释为对该子区域上约化态的任意量子电路制备进行经典模拟的复杂度。利用CFT谱的伪随机性和重算子插入的假设，我们观察到，在给定能量下，PET态相对于微正则密度矩阵的维格纳负性由$\boldsymbol{\text{exp}}\boldsymbol{\bigg[}\frac{\boldsymbol{1}}{\boldsymbol{8G_N}}\boldsymbol{(A_{\text{out}} - A_{\text{min}})\boldsymbol{\bigg]}}$给出，其中$A_{\text{out}}$是外极值曲面的面积，而$A_{\text{min}}$是最小极值曲面的面积。因此，在不存在Python午餐（bulk几何中的一种结构）时，边界子区域上约化密度矩阵的稳定子复杂度为$O(1)$，而在bulk几何中存在Python午餐时，该复杂度会呈指数级增强。
英文摘要
In this note, we study the stabilizer complexity of the reduced density matrix corresponding to one side of a partially entangled thermal (PET) state with fixed energy boundary conditions in a holographic CFT. In particular, we study Wigner negativity, an operationally meaningful magic monotone which can be interpreted as the complexity of classically simulating any quantum circuit preparation of the reduced state on the subregion. Using assumptions on the pseudorandomness of the CFT spectrum and the heavy operator insertion, we observe that the Wigner negativity of the PET state relative to the microcanonical density matrix at the given energy is given by $\exp\left[\frac{1}{8G_N}(A_{\text{out}} - A_{\text{min}})\right]$, where $A_{\text{out}}$ is the area of the outer extremal surface, while $A_{\text{min}}$ is the area of the minimal extremal surface. Thus, the stabilizer complexity of the reduced density matrix on the boundary subregion is $O(1)$ in the absence of a python's lunch, but gets exponentially enhanced in the presence of a python's lunch in the bulk geometry.
Comments12 pages, 2 Figures
