Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914171424079872 |
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| author | Cho, Kyoungho Bang, Jeongho |
| author_facet | Cho, Kyoungho Bang, Jeongho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation Cho, Kyoungho Bang, Jeongho Quantum Physics 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. |
| title | Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.21079 |