Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation

• URL: http://arxiv.org/abs/2511.21079v1
• Date: Wed, 26 Nov 2025 05:43:31 GMT
• Title: Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation
• Abstract summary: We develop a unified framework to analyze quantum teleportation through the joint geometry of two complementary figures of merit.<n>In particular, any measured pair $(F D)$ can be ported into a visibility estimate for isotropic resources.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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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