Simulations of closed timelike curves

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.

15 pages, 1 figure, accepted for publication in Foundations of Physics

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Cited by in corpus (8)

• Fast optimization algorithms and the cosmological constant
• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Agnostic Phase Estimation
• Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves
• The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems
• Reality, Causality, and Quantum Theory
• Revisiting Integer Factorization using Closed Timelike Curves
• Distinguishing quantum states using time travelling qubits in a presence of thermal environments