Detectability Limits for Intra-Block Temporal Drift in Finite-Key Entanglement-Based QKD

Abstract

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 $(\alpha ,\beta )$, we formulate a minimax hypothesis-testing problem and define the minimal detectable amplitude. We derive matching lower and upper bounds yielding ${\delta }_{\min }(n,\alpha ,\beta )=\Theta (n^{-1/2})$: if $n{\delta }^2\to 0$, no level-$\alpha$ 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.

13 pages, 6 figures