A graph-separation theorem for quantum causal models

Author(s): J. Pienaar, Č. Brukner

Journal: New Journal of Physics

Volume: 17

Page(s): 073020

Year: 2014

DOI Number: 10.1088/1367-2630/17/7/073020

Link: Link to publication

Abstract:

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 & 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 generalised 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. We note that the resulting model is still unable to give a faithful representation of correlations stronger than quantum mechanics, such as the Popescu-Rorlich box.

Note: http://arxiv.org/abs/1406.0430

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