AI 中文总结
研究量子优势声明的鲁棒性，将经典策略与基准相关性形式化为基准依赖性。给出有界奖励任务等的相关边界及扩展框架，应用于IBM硬件数据，还分析非贝尔量子核基准，将量子 - 经典分数分离转化为经典信息定量下限。
AI 中文摘要
量子优势的声明应该保持稳健，即使经典策略可以获取与评估基准相关的辅助信息，就像贝尔认证必须考虑测量依赖性一样。我们将这种相关性形式化为基准依赖性，它是测量依赖性在任务层面的推广。对于每个有界奖励任务，我们表明最优的依赖基准的经典分数服从\(S_\eta\leq\min\{1,S_{\mathrm{cl}}+\eta\}\)，并构建了一族饱和此边界的任务，表明在没有进一步假设的情况下，对\(\eta\)的线性依赖性是紧密的。对于具有逐轮依赖性的重复乘积任务，我们得到更强的乘法边界\(S_\eta^{(n)}\leq(\omega_{\mathrm c}+\eta)^n\)，并将框架扩展到有限样本数据、互信息约束、多方任务以及沿因果路径分布中的相关性。将这些结果应用于聚合的IBM硬件数据，我们得到CHSH的原始计数循环乘积证书为0.0812，Mermin - GHZ的为0.2178，而九宫格魔术方结构仍未得到认证；读出缓解值作为灵敏度估计单独报告。我们还分析了一个非贝尔量子核基准，其中一个标签构建变量的测量条件依赖性\(\widehat{\eta}_{\lambda}^{(Y)} = 0.5\)，高于报告的分数差距所需的阈值\(\eta_{\mathrm{req}} = 0.375\)，并产生完美的经典分类。因此，该框架将量子 - 经典分数分离转换为解释分数分离所需的与基准相关的经典信息的定量下限。
英文摘要
Claims of quantum advantage should remain robust even when classical strategies have access to side information correlated with the benchmark under evaluation, just as Bell certification must account for measurement dependence. We formalize such correlations as benchmark dependence, a task-level generalization of measurement dependence. For every bounded-reward task, we show that the optimal benchmark-dependent classical score obeys $S_η\leq\min\{1,S_{\mathrm{cl}}+η\}$, and construct a family of tasks that saturates this bound, showing that the linear dependence on $η$ is tight without further assumptions. For repeated product tasks with roundwise dependence, we obtain the stronger multiplicative bound $S_η^{(n)}\leq(ω_{\mathrm c}+η)^n$, and extend the framework to finite-sample data, mutual-information constraints, multipartite tasks, and correlations distributed along a causal path. Applying these results to aggregated IBM hardware data, we obtain positive raw-count cycle-product certificates of 0.0812 for CHSH and 0.2178 for Mermin--GHZ, while the nine-context magic-square construction remains uncertified; readout-mitigated values are reported separately as sensitivity estimates. We also analyze a non-Bell quantum-kernel benchmark, where a label-construction variable has measured conditional dependence $\widehatη_λ^{(Y)}=0.5$, above the threshold $η_{\mathrm{req}}=0.375$, required to close the reported score gap, and yields perfect classical classification. The framework therefore converts a quantum--classical score separation into a quantitative lower bound on the benchmark-correlated classical information required to explain the score separation.
Comments18 pages, 2 figures
