自测试的算子代数表述
An operator-algebraic formulation of self-testing
AI总结：
本文基于 $C^*$-代数上的状态提出了一种相关性自测试的新定义，证明了其在特定条件下与标准定义等价，并自然扩展至交换算子模型，揭示了有限维与无限维自测试之间的联系。
摘要：
我们给出了一个关于相关性的自测试的新定义，该定义基于 $C^*$-代数上的状态。我们证明，对于任何闭的有限维量子模型类，只要相关性是极值的且在该类中具有满秩模型，此定义便等价于标准定义。后一条件对于 POVM 量子模型类自动成立，但根据 Baptista, Chen, Kaniewski, Lolck, Mančinska, Gabelgaard Nielsen 和 Schmidt 的结果，对于投影模型类并不一定成立。对于极值二元相关性和极值同步相关性，我们证明任何针对投影模型的自测试也是针对 POVM 模型的自测试。是否存在针对投影模型而非 POVM 模型的自测试，这一问题仍然悬而未决。我们新定义的一个优势是它自然地扩展到了交换算子模型。我们证明，一个极值相关性是有限维量子模型的自测试，当且仅当它是有限维交换算子模型的自测试，并且还观察到许多已知的有限维自测试实际上也是无限维交换算子模型的自测试。
英文摘要：
We give a new definition of self-testing for correlations in terms of states on $C^*$-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does not necessarily hold for the class of projective models by a result of Baptista, Chen, Kaniewski, Lolck, Man{č}inska, Gabelgaard Nielsen, and Schmidt. For extremal binary correlations and for extremal synchronous correlations, we show that any self-test for projective models is a self-test for POVM models. The question of whether there is a self-test for projective models which is not a self-test for POVM models remains open. An advantage of our new definition is that it extends naturally to commuting operator models. We show that an extremal correlation is a self-test for finite-dimensional quantum models if and only if it is a self-test for finite-dimensional commuting operator models, and also observe that many known finite-dimensional self-tests are in fact self-tests for infinite-dimensional commuting operator models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
