Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause process $\textit{is not}$ equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

中文翻译：

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没有经典的常见原因或直接原因解释的简单且最稳健的过程

在因果关系相干叠加直觉的指导下，最近的工作提出了没有经典共因和直接原因解释的量子过程，即不能写成量子共因和量子直接因果关系的概率混合的过程。中央结算公司）。在这项工作中，我们分析了量子过程不能接受 CCDC 解释并提出“简单”过程的最低要求，我们证明这些过程是对一般噪声最稳健的过程。这些简单的过程可以通过准备一个最大纠缠态并应用恒等量子通道来实现，因此不需要明确的共因和直接原因的相干混合，利用一个过程同时具有这两种关系的可能性。然后我们证明，尽管所有的二分直接原因过程都是二分可分算子，但存在不是直接原因的二分可分过程。这表明决定天气进程的问题是直接导致进程 $\textit{is not}$ 等价于纠缠证明，并指出了纠缠方法检测非经典 CCDC 进程的局限性。我们还提出了一个半定的编程层次结构，可以检测和量化每个非经典 CCDC 过程的非经典 CCDC 鲁棒性。在其他结果中，我们的数值方法使我们能够证明这里介绍的简单过程可能也是对白噪声的最大鲁棒性。最后，我们探讨了二分直接原因过程和没有量子记忆的二分过程之间的等价性，