Simulations of closed timelike curves

TL;DR

This paper compares different models of closed timelike curves (CTCs), showing their equivalences and proposing methods to simulate them using quantum computers, which could enable experimental tests and clarify theoretical ambiguities.

Contribution

It proves the physical equivalence of T-CTCs and P-CTCs, and introduces a quantum simulation method for Deutschian CTCs with feasible overhead.

Findings

T-CTCs are equivalent to P-CTCs in simulation and information processing.

Quantum computers can simulate Deutschian CTCs with reasonable overhead in some cases.

An explicit maximum-entropy state for CTC systems is provided.

Abstract

Proposed models of closed timelike curves (CTCs) have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs) are physically equivalent to postselection CTCs (P-CTCs), in the sense that one model can simulate the other with reasonable overhead. As a consequence, their information-processing capabilities are equivalent. We also describe a method for quantum computers to simulate Deutschian CTCs (but with a reasonable overhead only in some cases). In cases for which the overhead is reasonable, it might be possible to perform the simulation in a table-top experiment. This approach has the benefit of resolving some ambiguities associated with the equivalent circuit model of Ralph et al. Furthermore, we provide an explicit form for the state of the CTC system such that it is a maximum-entropy state, as prescribed by Deutsch.