Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and the conditional mutual information of observed variables to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. As an application, we consider a system of three entangled qubits and transmit the second and third qubits over separate noisy quantum channels. In this model, we validate that the first qubit is a latent confounder and the common cause of the second and third qubits. In contrast, when two entangled qubits are prepared and one of them is sent over a noisy channel, there is no common confounder. We also demonstrate that the proposed approach outperforms the results of classical causal inference for the Tubingen database when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions. Thus, the proposed approach unifies classical and quantum causal inference in a principled way.
翻译:量子因果关系是一个新兴的研究领域,它有可能大大增进我们对量子系统的理解。在本文中,我们提出了一个理论框架,通过利用昆虫原则,将量子信息科学和因果推断结合起来。为此目的,我们利用隐性原因的灵球与观察到的变量的有条件相互信息之间的权衡,以发展一种可伸缩的算法方法,用以在量子系统中潜在混淆者(共同原因)出现的情况下推断因果关系。作为一种应用,我们考虑的是三个缠绕的象方块的系统,并传播第二和第三方位的二次和第三次方位,而不是分开的噪音量子渠道。在这个模型中,我们确认第一个qubit是一种潜在的混淆物,是第二和第三方位的共同原因。相反,当两个相缠绕的象项已经准备好,其中之一被发送到音量子系统(共同原因)存在时,没有常见的比较者。我们还发现,拟议的方法超出了图宾根数据库的典型因果结果,而当变量是利用正统的概率分配方式时,而不是通过正统的量基质分布,而不是通过正统的基质的基质分布来分析。