发表机构
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area; QMATH, Department of Mathematical Sciences, University of Copenhagen（粤港澳大湾区量子科学中心; 哥本哈根大学数学科学学院 QMATH）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明单一量子关联的精确自检验不蕴含鲁棒自检验，通过算子代数构造同步二元关联，并利用迹态刻画给出反例。
AI 中文摘要
我们证明，量子关联的精确自检验并不蕴含鲁棒自检验。Mančinska 和 Schmidt 先前已针对非局域博弈建立了这种分离，但他们的鲁棒性障碍源于两个不同的最优关联，其中被自检验的关联仍是鲁棒的。我们针对单一关联建立了这种分离。我们的证明采用算子代数方法。主要技术贡献是一个一般性构造，该构造将任意有限表示的、具有酉生成元和实系数关系的 C*-代数关联到一个同步二元关联。该关联的实现态恰好对应于代数上的迹态。我们将此构造应用于一个具有唯一有限维迹态和另一个不同的 amenable 迹态的代数。根据 Zhao 以及独立地 Kar 所建立的刻画，所得的关联是一个自检验，但不是鲁棒自检验。
英文摘要
We show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation. Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.
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