Witness wedges in fidelity-deviation plane: Separating teleportation advantage and Bell-inequality violation
Phys. Rev. A 113, 052458 – Published 29 May, 2026
DOI: https://doi.org/10.1103/q9d2-5zv4
Abstract
We develop a unified framework to analyze -dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity (how well a protocol works on average) and fidelity deviation (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation-symmetry calculus that reduces the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for and 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, within the isotropic-noise model, any measured pair can be ported into a visibility estimate for isotropic-channel resources, turning the plane into a calibrated diagnostic map. We further cast the teleportation advantage and Collins–Gisin–Linden–Massar–Popescu (CGLMP) [Collins et al., Phys. Rev. Lett. 88, 040404 (2002)] inequality violation as two witness lines in the plane: one line certifies that beats the classical benchmark , 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.
