发表机构
Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（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
本文构造非局域博弈，证明全秩投影测量自检验与无假设自检验存在分离，并解决相关猜想，同时表明全秩 PVM 自检验不稳健。
AI 中文摘要
我们构造了一个非局域博弈，该博弈在纯全 Schmidt 秩投影策略中自检验最大纠缠量子比特策略，但允许使用一个非投影测量实现不等价的最优解。这解决了 Baptista 等人关于同时施加全秩和投影性的猜想。该构造将 CHSH 与一个辅助博弈 $G$ 相结合，$G$ 在这些假设下迫使确定性答案，并在没有这些假设时允许 trine POVM 最优解。我们将 $G$ 的最优关联分类为由 $\mathbb{C}\oplus M_2(\mathbb{C})$ 的迹态参数化的线段。状态支撑上的投影性移除矩阵加项，而具有非零非中止概率的投影膨胀具有非迹局部态，其零左理想不是双侧的。最后，局部维度为六的一个族表明全秩 PVM 自检验不是稳健的。
英文摘要
We construct a nonlocal game that self-tests a maximally entangled qubit strategy among pure full-Schmidt-rank projective strategies, but admits an inequivalent optimum using one nonprojective measurement. This resolves a conjecture of Baptista et al. on imposing full rank and projectivity simultaneously. The construction combines CHSH with an auxiliary game $G$ that forces deterministic answers under these assumptions and admits a trine POVM optimum without them. We classify the optimal correlations of $G$ as a line segment parametrized by the tracial states of $\mathbb{C}\oplus M_2(\mathbb{C})$. Projectivity on the state support removes the matrix summand, whereas projective dilations with nonzero nonabort probability have a nontracial local state whose zero left ideal is not two-sided. Finally, a family in local dimension six shows that the full-rank PVM self-test is not robust.
Comments18 pages
