More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here, we give an answer to this question for temporal processes that are probed sequentially by means of projective measurements of the same observable. Defining classical processes as those that can, in principle, be simulated by means of classical resources only, we fully characterize the set of such processes. Based on this characterization, we show that for non-Markovian processes (i.e., processes with memory), the absence of coherence does not guarantee the classicality of observed phenomena; furthermore, we derive an experimentally and computationally accessible measure for nonclassicality in the presence of memory. We then provide a direct connection between classicality and the vanishing of quantum discord between the evolving system and its environment. Finally, we demonstrate that—in contrast to the memoryless setting—in the non-Markovian case, there exist processes that are genuinely quantum; i.e., they display nonclassical statistics independent of the measurement scheme that is employed to probe them.

中文翻译：

---

非马尔可夫量子过程何时是经典的？

量子理论诞生后的一个多世纪，关于哪些特征和现象从根本上说是量子的问题仍在争论之中。在这里，我们针对这个时间过程的问题给出了答案，这些时间过程是通过对相同可观测值的投影测量来顺序探查的。将经典过程定义为原则上只能通过经典资源进行模拟的过程，我们充分表征了这些过程的集合。基于这种表征，我们表明对于非马尔可夫过程（即具有记忆的过程），缺乏连贯性并不能保证观察到的现象的经典性。此外，我们导出了存在内存时非经典性的实验和计算可访问性度量。然后，我们提供了经典性与进化系统及其环境之间量子不和谐的消失之间的直接联系。最后，我们证明，与无记忆的情况相比，在非马尔可夫情形下，存在的过程确实是量子的。也就是说，它们显示非经典统计信息，而与用来探测它们的测量方案无关。