While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

中文翻译：

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真正的多方时间纠缠

虽然已经对空间量子相关性进行了非常详细的研究，但对时间过程可以展示的真正量子相关性知之甚少。使用量子梳形式主义，时间过程可以映射到量子态，关键的区别在于时间相关性必须满足因果排序，而它们的空间对应物不受相同方式的约束。在这里，我们利用这种等价性并使用多部分纠缠理论的工具来提供（因果排序的）时间量子过程可以显示的相关性结构的全面图景。第一的，关注在两个时间点探测的过程的情况——可以等效地用三方量子态来描述——我们为不同分裂中二分纠缠的存在提供了必要和充分的条件。接下来，我们将这些场景与之前研究的量子存储器、纠缠破坏超级通道和量子转向等概念联系起来，从而为时间量子过程中的纠缠提供了物理解释，并确定了其创建所需的资源。此外，我们构建了 W 型和 GHZ 型真正多分纠缠二次过程的明确例子，并证明时间过程中真正的多分纠缠可以是一种紧急现象。最后，