见证楔在保真度-偏差平面中的应用：分离量子 teleportation 优势与贝尔不等式违反
Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation
AI总结：
本文提出统一框架分析d维量子 teleportation，通过两个互补指标的几何联合分析平均保真度F和保真度偏差D，推导出闭式表达式并给出紧密界限，将(F,D)平面转化为校准诊断图，分离teleportation优势与贝尔不等式违反。
摘要：
我们开发了一个统一框架来分析d维量子 teleportation，通过两个互补指标的几何联合分析平均保真度F（协议在平均上的表现）和保真度偏差D（在输入上的均匀性）。技术上，我们基于Schur-Weyl对偶性和排列对称性微积分构建了表示论框架，将高阶矩Haar平均减少为由复合修正幺正算符的迹不变量组成的有限集合。这为任意希尔伯特空间维度下F和D提供了闭式表达式，并给出了紧密界限，将允许的偏差直接与最优平均性能的差距联系起来。特别是，任何测量对(F,D)可以转换为各向同性信道资源的可见性估计，将(F,D)平面转化为校准诊断图。我们进一步将teleportation优势和CGLMP不等式违反作为(F,D)平面中的两个见证线：一条线证明F超过经典基准2/(d+1)，另一条线证明贝尔非局域性。它们相同的斜率但不同的截距揭示了“纠缠却局域”和“真正非局域”资源之间的定量差距。
英文摘要：
We develop a unified framework to analyze $d$-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity $F$ (how well a protocol works on average) and fidelity deviation $D$ (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for $F$ and $D$ in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair $(F, D)$ can be ported into a visibility estimate for isotropic channel resources, turning the $(F, D)$-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the $(F,D)$ plane: one line certifies that $F$ beats the classical benchmark $2/(d{+}1)$, while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.
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