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There has been considerable recent interest in the consequences of closedtimelike curves (CTCs) for the dynamics of quantum mechanical systems. A vastmajority of research into this area makes use of the dynamical equationsdeveloped by Deutsch, which were developed from a consistency condition thatassumes that mixed quantum states uniquely describe the physical state of asystem. We criticise this choice of consistency condition from an epistemicperspective, i.e., a perspective in which the quantum state represents a stateof knowledge about a system. We demonstrate that directly applying Deutsch'scondition when mixed states are treated as representing an observer's knowledgeof a system can conceal time travel paradoxes from the observer, rather thanresolving them. To shed further light on the appropriate dynamics for quantumsystems traversing CTCs, we make use of a toy epistemic theory with a strictlyclassical ontology due to Spekkens and show that, in contrast to the results ofDeutsch, many of the traditional paradoxical effects of time travel arepresent.

Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective