A sideways look at faithfulness for quantum correlations

Despite attempts to apply the lessons of causal modelling to the observed correlations typical of entangled bipartite quantum systems, Wood and Spekkens argue that any causal model purporting to explain these correlations must be fine tuned; that is, it must violate the assumption of faithfulness. The faithfulness assumption is a principle of parsimony, and the intuition behind it is basic and compelling: when no statistical correlation exists between the occurrences of a pair of events, we have no reason for supposing there to be a causal connection between them. This paper is an attempt to undermine the reasonableness of the assumption of faithfulness in the quantum context. Employing a symmetry relation between an entangled bipartite quantum system and a `sideways' quantum system consisting of a single photon passing sequentially through two polarisers, I argue that Wood and Spekkens' analysis applies equally to this sideways system. If this is correct, then the consequence endorsed by Wood and Spekkens for an ordinary entangled quantum system amounts to a rejection of a causal explanation in the sideways, single photon system, too. Unless rejecting this causal explanation can be sufficiently justified, then it looks as though the sideways system is fine tuned, and so a violation of faithfulness in the ordinary entangled system may be more tolerable than first thought. Thus extending the classical `no fine-tuning' principle of parsimony to the quantum realm may well be too hasty.