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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.24230 |
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| _version_ | 1866913157922947072 |
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| author | Marcelino, Rafael Duarte Garcia, Julio Smanioto Rufino, Matheus |
| author_facet | Marcelino, Rafael Duarte Garcia, Julio Smanioto Rufino, Matheus |
| contents | We study the statistical detectability of intra-block temporal drift in finite-key entanglement-based quantum key distribution, with particular relevance to E91-type parameter estimation and monitoring. Drift is modeled as a mean-preserving Lipschitz perturbation of Bernoulli observables, capturing structured temporal variation that is invisible to global-average tests. For a block of size $n$ and confidence levels $(α,β)$, we formulate a minimax hypothesis-testing problem and define the minimal detectable amplitude. We derive matching lower and upper bounds yielding $δ_{\min}(n,α,β)=Θ(n^{-1/2})$: if $nδ^2 \to 0$, no level-$α$ procedure can guarantee nontrivial uniform power over the admissible drift class, whereas a calibrated CUSUM statistic detects drift at the matching scale. Explicit constants for linear, sinusoidal, and step profiles, together with simulations, confirm the predicted scaling collapse. The result quantifies a finite-block monitoring-resolution limit and is distinct from composable security certification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24230 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Detectability Limits for Intra-Block Temporal Drift in Finite-Key Entanglement-Based QKD Marcelino, Rafael Duarte Garcia, Julio Smanioto Rufino, Matheus Quantum Physics 81P94, 62G10, 62L10 E.3; G.3 We study the statistical detectability of intra-block temporal drift in finite-key entanglement-based quantum key distribution, with particular relevance to E91-type parameter estimation and monitoring. Drift is modeled as a mean-preserving Lipschitz perturbation of Bernoulli observables, capturing structured temporal variation that is invisible to global-average tests. For a block of size $n$ and confidence levels $(α,β)$, we formulate a minimax hypothesis-testing problem and define the minimal detectable amplitude. We derive matching lower and upper bounds yielding $δ_{\min}(n,α,β)=Θ(n^{-1/2})$: if $nδ^2 \to 0$, no level-$α$ procedure can guarantee nontrivial uniform power over the admissible drift class, whereas a calibrated CUSUM statistic detects drift at the matching scale. Explicit constants for linear, sinusoidal, and step profiles, together with simulations, confirm the predicted scaling collapse. The result quantifies a finite-block monitoring-resolution limit and is distinct from composable security certification. |
| title | Detectability Limits for Intra-Block Temporal Drift in Finite-Key Entanglement-Based QKD |
| topic | Quantum Physics 81P94, 62G10, 62L10 E.3; G.3 |
| url | https://arxiv.org/abs/2605.24230 |