发表机构
The Hong Kong University of Science and Technology (Guangzhou); Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（香港科技大学（广州）; 粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造有理系数贝尔泛函，实现局域维度2下量子比特POVM与投影测量的解析分离，得到大于1/1000的认证间隙，还证明对应策略达到量子最优值。
AI 中文摘要
广义测量可通过扩大希尔伯特空间后以投影方式实现，但这种扩张会改变可用的局域维度。我们构造了一个有理系数的贝尔泛函，其在局域维度2时可区分两种测量模型。一个具有有理矩阵元的显式三结果量子比特正算子值测量（POVM）达到$2\sqrt{2}+1/100$。另一方面，所有量子比特投影策略的界为$2\sqrt{2}+\sqrt{5}/250+\sqrt{2}/32400$，从而得到一个大于$1/1000$的完全解析认证间隙。据我们所知，这是首个在任意共享两量子比特态上实现量子比特POVM与量子比特投影测量完全解析贝尔泛函分离的工作。为完整性起见，提供了分离定理的Lean证明。此外，一个精确的3阶非交换平方和（noncommutative sum-of-squares）证明，该显式量子比特策略达到了无约束有限维张量积量子最优值。
英文摘要
Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional with rational coefficients that separates the two measurement models at local dimension two. An explicit three-outcome qubit positive-operator-valued measure with rational matrix entries attains $2\sqrt2+1/100$. On the other hand, all qubit-projective strategies are bounded by $2\sqrt2+\sqrt5/250+\sqrt2/32400$, giving a fully analytic certified gap greater than $1/1000$. To our knowledge, this is the first fully analytic Bell-functional separation between qubit POVMs and qubit projective measurements over arbitrary shared two-qubit states. Lean certificate for the separation theorem is provided for completeness. Separately, an exact level-3 noncommutative sum-of-squares certificate proves that the explicit qubit strategy attains the unrestricted finite-dimensional tensor-product quantum optimum.
Comments9 pages. Comments are welcome
