It was recently found that the indefinite causal order in the quantum switch can be certified device-independently when assuming the impossibility of superluminal influences. Here we strengthen this result in two ways. First, we give a proof of this fact which is possibilistic rather than probabilistic, i.e. which does not rely on the validity of probability theory at the hidden variable level. Then, returning to the probabilistic setting, we show that the indefinite causal order in the quantum switch is also maximal, in the sense that the observed correlations are incompatible even with the existence of a causal order on only a small fraction of the runs of the experiment. While the original result makes use of quantum theory's violation of a Clauser-Horne-Shimony-Holt inequality, the proofs presented here are based on Greenberger, Horne, and Zeilinger's and Mermin's proofs of nonlocality, respectively.

中文翻译：

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量子开关中的可能和最大不确定因果顺序


最近发现，当假设超光速影响是不可能的时，量子开关中的不确定因果顺序可以独立于器件进行认证。在这里，我们通过两种方式来强化这一结果。首先，我们给出了这个事实的证明，它是可能性的而不是概率性的，即它不依赖于概率论在隐藏变量层面的有效性。然后，回到概率设置，我们证明量子开关中的不确定因果顺序也是最大的，从某种意义上说，观察到的相关性是不相容的，即使只在实验的一小部分运行中存在因果顺序。虽然原始结果利用了量子理论对 Clauser-Horne-Shimony-Holt 不等式的违反，但这里提供的证明分别基于 Greenberger、Horne 以及 Zeilinger 和 Mermin 的非局域性证明。