发表机构
The First Affiliated Hospital of Xi’an Jiaotong University; Xi’an Jiaotong University（西安交通大学第一附属医院; 西安交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明Alice条件化Bell证书在有限层级下无法完全认证标准二级证书，导致无界次数开销，并给出倾斜CHSH场景下的增长下界及尖锐一级成本区间。
AI 中文摘要
要求每个平方和项仅涉及Alice的一个测量问题，可能会带来无界的认证成本。在最简单的Bell场景中，我们证明Alice条件化的NPA层级结构的任何有限层级都不包含所有标准二级Bell证书。在无限二面体群上，一个显式的截断正泛函族在每一个预先指定的有限层级上都超过倾斜CHSH量子界，而标准二次证书则是精确的。一个Fejer加权迹将正性归结为从移动平均Gram矩阵中减去一个秩一矩阵。所需的条件化层级在端点倾斜附近至少以$(2-\alpha)^{-1/2}$的速度增长。这限制了编译游戏可靠性证明中精确nice-SOS输入的次数。因此，没有有限的条件化层级能够针对量子边信息认证整个最优CHSH随机性权衡，尽管标准二级可以做到。在远离端点处，我们证明在整个$\alpha\in[13/10,3/2]$区间内存在一个尖锐的一级成本，使用最优策略核和精确的Bernstein矩阵正性来认证一个连续区间。这些结果将普通SOS次数与由单问题证书结构所决定的资源区分开来。
英文摘要
The degree needed to certify a quantum Bell bound can diverge evenwhen a fixed-degree unrestricted certificate exists. We identify the geometry of optimal-strategy contacts as the source of this cost in Alice-conditioned sum-of-squares certificates. For tilted CHSH, the exact degree grows as $Θ((2-α)^{-1/2})$ when the tilt is on Alice, but remains one after exchanging the parties. For asymmetric correlator weight $λ>1$, one finite level covers every tilt; its minimum grows as $Θ((λ-1)^{-1/2})$ and equals two precisely when $λ\geq\sqrt5/2$. Matching bounds follow fromtruncated positive functionals, a necessary contact-derivative bound, and polynomial cancellation of exterior poles. A contact-preserving approximation theorem extends the sufficient mechanism beyond these examples. The resulting degree costs control certification of full device-independent randomness curves; in the symmetric family the worst Bell and guessing-probability errors scale as $Θ(k^{-4})$. The results quantify the cost of conditional-block information and its scope within the nice-SOS route to compiled-game soundness.
