模拟极值时间相关
Simulating extremal temporal correlations
摘要：
由单个量子系统的连续测量产生的相关性形成了一个多面体。这是由时间箭头（AoT）约束定义的，这意味着未来对测量设置的选择不能影响过去的结果。我们讨论了所需的资源，以模拟极端点的AoT多面体，其中的资源是量化的最小尺寸，或“内部存储器”的物理系统。首先，我们分析了对称性下极值点的等价类。其次，我们刻画了获得AoT多面体的给定极值点所需的最小维数，包括长序列渐近极限的尺度下界。最后，我们提出了一个一般的方法来获得较长的序列的维数敏感的时间不等式，基于较短的不等式，并研究其鲁棒性的缺陷。
英文摘要：
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.
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