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

TL;DR

This paper introduces a geometric framework analyzing quantum teleportation fidelity and deviation, linking these metrics to channel resources and Bell nonlocality, providing new bounds and diagnostic tools for quantum communication.

Contribution

It develops a unified, representation-theoretical framework for analyzing teleportation performance metrics and their relation to Bell inequality violations in arbitrary dimensions.

Findings

Closed-form expressions for fidelity and deviation in any dimension.

Tight bounds linking fidelity deviation to performance gap.

Witness lines in the (F,D) plane for teleportation advantage and Bell nonlocality.

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.