Open timelike curves violate Heisenberg's uncertainty principle

TL;DR

This paper demonstrates that open timelike curves (OTCs) can violate Heisenberg's uncertainty principle, enabling perfect state discrimination and cloning, and explores their implications as a novel quantum-gravity model.

Contribution

It introduces OTCs as a simplified model that violates fundamental quantum principles and extends the framework to wave-packets, connecting quantum mechanics with gravitational effects.

Findings

OTCs violate Heisenberg's uncertainty principle.

OTCs enable perfect cloning and state discrimination.

Model recovers standard quantum mechanics in a physical limit.

Abstract

Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave-packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time-dilation suggests that OTCs provide a novel alternative to existing proposals for the behaviour of quantum systems under gravity.