Quantum no-go theorems in causality respecting systems in presence of closed timelike curves: Tweaking the Deutsch condition

TL;DR

This paper explores the impact of closed timelike curves on causality respecting quantum systems within the Deutsch model, revealing violations of no-cloning and no-deleting, and proposing a modified model that enables approximate teleportation.

Contribution

It introduces concepts of quantum information popping up and elimination, and shows how these lead to violations of fundamental quantum no-go theorems in CTC interactions, proposing a tweak to the Deutsch model.

Findings

No-cloning and no-deleting are violated in CTC-interacting systems.

Limits are established on entanglement creation involving CTCs.

A modified Deutsch model allows for approximate teleportation beyond classical limits.

Abstract

We consider causality respecting (CR) quantum systems interacting with closed timelike curves (CTCs), within the Deutsch model. We introduce the concepts of popping up and elimination of quantum information and use them to show that no-cloning and no-deleting, which are true in CR quantum systems, are no more valid in the same that are interacting with CTCs. We also find limits on the possibility of creation of entanglement between a CR system and a CTC, and the same between two CR systems in the presence of a CTC. We prove that teleportation of quantum information, even in its approximate version, from a CR region to a CTC is disallowed. Interestingly, we find that tweaking the Deutsch model, by allowing the input and output to be not the same, leads to a nontrivial approximate teleportation beyond the classical limit.