The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or "internal memory" of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections.

中文翻译：

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模拟极值时间相关性

对单个量子系统的连续测量产生的相关性形成了多面体。这是由时间箭头 (AoT) 约束定义的，这意味着未来的测量设置选择不能影响过去的结果。我们讨论了模拟 AoT 多胞体极值点所需的资源，其中资源根据物理系统的最小维度或“内部存储器”进行量化。首先，我们分析对称下极值点的等价类。其次，我们描述了获得 AoT 多胞体的给定极值点所需的最小维度，包括长序列渐近极限的下标度界限。最后，我们提出了一种通用方法，基于较短序列的不等式，推导出较长序列的维度敏感时间不等式，