发表机构
University of Waterloo; Perimeter Institute for Theoretical Physics（滑铁卢大学; 圆周理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析了自洽纠缠认证协议的复杂性，证明了在固定维度下达到特定纠缠分辨率所需的效应数量与目标态副本数的缩放关系，并指出在恒等式未知时的最优样本复杂性仍待解决。
AI 中文摘要
在近期工作 Phys. Rev. X 16, 031057 (2026) 中，我们提出了一种基于广义非语境性的自洽纠缠认证方法。该方法无需预先表征测量设备，并且，在能够访问所有局域测量的条件下，可以认证贝尔电路中的每一个纠缠态。在此，我们研究该协议在有限实验中的复杂性。在固定局域维度 $d$ 下，我们证明，要达到迹距离纠缠分辨率 $\gamma$，所需的不同局域效应的最优数量为 $\Theta_d(\gamma^{-(d-1)})$。即使测量是针对目标态定制的，这种缩放也是必要的。独立的 Haar 随机投影测量则需要 $\Theta_d(\gamma^{-(d-1)}\log(1/\gamma))$ 个效应。最后，我们证明，一旦确切的操作恒等式已知，对于错误概率至多为 $\delta$ 的认证，目标态的 $\Theta_d(\gamma^{-2}\log(1/\delta))$ 个副本是必要且充分的。当这些恒等式必须从相同的有限目标态数据中推断时，确定最优样本复杂性仍然是一个开放问题。
英文摘要
In recent work Phys. Rev. X 16, 031057 (2026), we proposed a self-consistent approach to entanglement certification based on generalized noncontextuality. It requires no prior characterization of the measurement devices and, given access to all local measurements, can certify every entangled state in a Bell circuit. Here, we study the complexity of this protocol in a finite experiment. At fixed local dimension $d$, we show that the optimal number of distinct local effects needed to reach a trace-distance \textit{entanglement resolution} $γ$ is $Θ_d(γ^{-(d-1)})$. This scaling is necessary even when the measurements are tailored to the target state. Independent Haar-random projective measurements instead require $Θ_d(γ^{-(d-1)}\log(1/γ))$ effects. Finally, we show that, once the exact operational identities are known, $Θ_d(γ^{-2}\log(1/δ))$ copies of the target state are necessary and sufficient for certification with error probability at most $δ$. Determining the optimal sample complexity when those identities must instead be inferred from the same finite target-state data remains open.
CommentsPreliminary version for upcoming talks
