A graph-separation theorem for quantum causal models
A graph-separation theorem for quantum causal models
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DOI：
10.1088/1367-2630/17/7/073020
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发表时间：
2014-06
影响因子：
3.3
通讯作者：
J. Pienaar;Č. Brukner
中科院分区：
文献类型：
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作者：
J. Pienaar;Č. Brukner
因果模型是物理系统作为有向无环图 (DAG) 的抽象表示，其中统计依赖性使用称为“d-分离”的图形标准进行编码。 Wood 和 Spekkens 最近的工作表明，因果模型一般不能忠实地表示量子系统。由于 d 分离编码了赖兴巴赫共因原理（RCCP）的一种形式，其有效性在量子力学中值得怀疑，因此我们提出了一种不假设 RCCP 的广义图分离规则。我们证明新规则忠实地捕获了量子网络中可观测值之间的统计依赖性，编码为 DAG，并在经典极限下简化为 d 分离。
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called ‘d-separation’. Recent work by Wood and Spekkens shows that causal models cannot, in general, provide a faithful representation of quantum systems. Since d-separation encodes a form of Reichenbach’s common cause principle (RCCP), whose validity is questionable in quantum mechanics, we propose a generalized graph separation rule that does not assume the RCCP. We prove that the new rule faithfully captures the statistical dependencies between observables in a quantum network, encoded as a DAG, and reduces to d-separation in a classical limit.