QuIC, Ecole Polytechnique de Bruxelles, C.P. 165, Université Libre de Bruxelles, 1050, Brussels, Belgium.
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000, Grenoble, France.
Nat Commun. 2023 Mar 16;14(1):1471. doi: 10.1038/s41467-023-36893-3.
It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how such processes can be realised in practice. In order to provide a rigorous framework for the notion that certain such processes have a realisation in standard quantum theory, the concept of time-delocalised quantum subsystem has been introduced. In this paper, we show that realisations on time-delocalised subsystems exist for all unitary extensions of tripartite processes. This class contains processes that violate causal inequalities, i.e., that can generate correlations that witness the incompatibility with definite causal order in a device-independent manner, and whose realisability has been a central open problem. We consider a known example of such a tripartite classical process that has a unitary extension, and study its realisation on time-delocalised subsystems. We then discuss this finding with regard to the assumptions that underlie causal inequalities, and argue that they are indeed a meaningful concept to show the absence of a definite causal order between the variables of interest.
已经表明，在理论上存在量子和经典过程，其中各个部分执行的操作不是按照明确定义的因果顺序发生的。一个核心问题是，这样的过程是否以及如何在实践中实现。为了为某些这样的过程在标准量子理论中具有实现提供一个严格的框架，引入了时移量子子系统的概念。在本文中，我们证明了对于三分过程的所有幺正扩展都存在时移子系统的实现。这个类包含违反因果不等式的过程，即可以以设备独立的方式生成与确定因果顺序不兼容的相关性，其实现一直是一个核心的开放性问题。我们考虑了这样一个三分经典过程的已知例子，它具有一个幺正扩展，并研究了它在时移子系统上的实现。然后，我们根据因果不等式的基础假设来讨论这个发现，并认为它们确实是一个有意义的概念，可以表明感兴趣的变量之间没有确定的因果顺序。
