A graph-separation theorem for quantum causal models. (July 2015)

• Record Type: Journal Article
• Authors: Pienaar, Jacques; Brukner, Časlav
• Is Part Of: New journal of physics. Volume 17:Number 7(2015:Jul.)
• Page Start: 11
• Page End: 24
• Publication Date: 2015-07
• Subjects: Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/17/7/073020
• Languages: English
• ISSNs: 1367-2630

Abstract

<abstract> <title>Abstract</title> <p>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 '<italic>d</italic>-separation'. Recent work by Wood and Spekkens shows that causal models cannot, in general, provide a faithful representation of quantum systems. Since <italic>d</italic>-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 <italic>d</italic>-separation in a classical limit.</p> </abstract>