Tsirelson问题
Tsirelson's Problem
摘要：
两个独立的观察者在联合量子系统上进行测量的情况通常使用张量积形式的希尔伯特空间来建模，每个因子与一个观察者相关联。相应地，描述可观测量的算符只作用于其中一个张量因子。然而，同样的情况也可以通过仅使用一个联合希尔伯特空间来建模，并且要求与不同观察者相关联的所有算子都是可交换的，即是联合可测量的而不会引起干扰。Tsirelson的问题是现在决定的问题是否所有的量子关联函数之间的两个独立的观察员来自可交换的观测值也可以表示使用观测定义的希尔伯特空间的张量积形式。Tsirelson已经表明，区别是无关的情况下，周围的希尔伯特空间是有限维。我们证明了这个问题等价于是否所有的量子关联函数都可以用有限维系统的关联函数来近似的问题。我们还讨论了一些物理的例子，满足这一要求。
英文摘要：
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing the observables are then acting non-trivially only on one of the tensor factors. However, the same situation can also be modelled by just using one joint Hilbert space, and requiring that all operators associated to different observers commute, i.e. are jointly measurable without causing disturbance. The problem of Tsirelson is now to decide the question whether all quantum correlation functions between two independent observers derived from commuting observables can also be expressed using observables defined on a Hilbert space of tensor product form. Tsirelson showed already that the distinction is irrelevant in the case that the ambient Hilbert space is of finite dimension. We show here that the problem is equivalent to the question whether all quantum correlation functions can be approximated by correlation function derived from finite-dimensional systems. We also discuss some physical examples which fulfill this requirement.
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