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

TL;DR

This paper critiques Deutsch's consistency condition for quantum states on closed timelike curves from an epistemic perspective, showing it can hide paradoxes, and demonstrates that classical epistemic models reveal traditional time travel paradoxes.

Contribution

It challenges the standard quantum approach to CTCs by analyzing the epistemic interpretation and introduces a classical epistemic model to highlight paradoxes.

Findings

Deutsch's condition can conceal time travel paradoxes

Classical epistemic models reveal traditional paradoxes

Critique of mixed states as knowledge representations

Abstract

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticise this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch's condition when mixed states are treated as representing an observer's knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.