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.
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