标题： 对物理学可能的影响：Tsirelson 问题的否定解决 显示英文标题

标题： Possible consequences for physics of the negative resolution of Tsirelson's problem

摘要： 2020年，Ji等人。 [arXiv:2001.04383和Comm.~ACM 64\}, 131 (2021)] 提供了一个证明，表明复杂性类$\text{MIP}^\ast$和$\text{RE}$是等价的。 这个结果意味着对Tsirelson问题的否定性解决，即$C_{qa}$（张量积相关性的闭包）和$C_{qc}$（交换相关性的集合）可以通过超平面（即贝尔不等式）分离。 特别是，存在由无限维量子系统上的交换测量（有限数量和有限结果）产生的相关性，这些相关性不能通过有限维张量积相关性的序列来近似。 在这里，我们指出该结果有四种逻辑可能性。 每种可能性都令人感兴趣，因为它们以不同的方式从根本上挑战了空间分离系统的本质。 我们列出了开放性问题，以推动对哪种可能性是正确的做出决定。 显示英文摘要

摘要： In 2020, Ji et al. [arXiv:2001.04383 and Comm.~ACM 64}, 131 (2021)] provided a proof that the complexity classes $\text{MIP}^\ast$ and $\text{RE}$ are equivalent. This result implies a negative resolution of Tsirelson's problem, that is, $C_{qa}$ (the closure of the set of tensor product correlations) and $C_{qc}$ (the set of commuting correlations) can be separated by a hyperplane (that is, a Bell-like inequality). In particular, there are correlations produced by commuting measurements (a finite number of them and with a finite number of outcomes) on an infinite-dimensional quantum system which cannot be approximated by sequences of finite-dimensional tensor product correlations. Here, we point out that there are four logical possibilities of this result. Each possibility is interesting because it fundamentally challenges the nature of spacially separated systems in different ways. We list open problems for making progress for deciding which of the possibilities is correct.