Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0908.2655 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Discontinuous quantum evolutions in the presence of closed timelike curves

Richard DeJonghe, Kimberly Frey, Tom D. Imbo

Published Apr 20, 2010• 8 citations
arXivHTMLPDF

Abstract

We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts nonlinear and nonunitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutsch's approach.

DOI
10.1103/physrevd.81.087501

Related papers

Quantum Closed Timelike Curves: Deutsch Model and Temporal Evolution

Mikhail Pavlov

Abstract This study examines closed timelike curves (CTCs) in quantum mechanics, focusing on the Deutsch model, one of the most widely studied frameworks for describing quantum systems in the presence of time loops. In this model, a quantum state ∣ψ⟩|\psi\rangle∣ψ⟩ interacts unitarily with its past version, effectively forming a two-qubit system where the chronologically consistent qubit interacts with a qubit ρCTC\rho_{\text{CTC}}ρCTC trapped in a closed timelike curve. The state ρCTC\rho_{\text{CTC}}ρCTC is determined by the Deutsch consistency condition, ensuring self-consistent evolution along the CTC. This approach allows for rigorous modeling of quantum systems under non-classical temporal structures, providing insights into temporal correlations, causality violations, and the potential computational advantages offered by CTC-assisted quantum operations. While alternative CTC models based on postselection have been proposed, the Deutsch model remains a foundational reference for studying quantum evolution in non-linear temporal frameworks. Its analysis informs research in quantum information, retrocausality, and the theoretical limits of computation in exotic spacetime geometries.

•Mar 4, 2026•0 citations

Quantum computational complexity in the presence of closed timelike curves

Dave Bacon

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D 44, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve $\mathit{NP}$-complete problems with only a polynomial number of quantum gates.

arXiv:quant-ph/0309189•Physical Review A•Sep 13, 2004•73 citations

Would Closed Timelike Curves Help to Do Quantum Cloning?

Angel Ricardo Plastino

The possibility of performing quantum cloning in the presence of closed time like curves is considered. We analyze a model of the quantum cloning process involving a source qubit, a target qubit, and a quantum copy machine which is itself a composite quantum system. A subsystem of the copy machine is allowed to traverse a closed time like curve. Under these circumstances the evolution of the chronology respecting parts of the system is nonlinear. This suggests (Deutsch, 1991) that quantum cloning might be possible. We prove that, if only one subsystem of the copy machine is allowed to traverse a closed time like curve and the copy machine’s Hilbert space is of finite dimension, universal quantum cloning is impossible.

AIP conference proceedings•Jan 1, 2006•5 citations

Nonlinearity in quantum theory and closed timelike curves

Michael J. Cassidy

We examine the consequences of the density matrix approach to quantum theory in the context of a model spacetime containing closed timelike curves. We find that, in general, an initially pure state will evolve in a nonlinear way to a mixed quantum state. CPT invariance and the implications of this nonlinearity for the statistical interpretation of quantum theory are discussed.

arXiv:gr-qc/9409003•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Nov 15, 1995•19 citations

Eigenvalue Formulation of Quantum Mechanics Near Closed Timelike Curves

Z. Gedik

Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.

arXiv:1201.4870•Jan 23, 2012•1 citation

Closed timelike curves in measurement-based quantum computation

Raphael Dias da Silva, Ernesto F. Galvão, Elham Kashefi

Many results have been recently obtained regarding the power of hypothetical closed timelike curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way the CTC model proposed by Bennett, Schumacher, and Svetlichny. We identify a class of CTCs in this model that can be simulated deterministically and point to a fundamental limitation of Deutsch's CTC model which leads to predictions conflicting with those of the one-way model.

arXiv:1003.4971•Physical Review A•Jan 24, 2011•16 citations
We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts nonlinear and nonunitary evolutions of the system, we demonstrate that it also gives rise to evolutions which are a discontinuous function of the input state. These discontinuities persist for the most natural modifications of Deutsch's approach.
Abstract This study examines closed timelike curves (CTCs) in quantum mechanics, focusing on the Deutsch model, one of the most widely studied frameworks for describing quantum systems in the presence of time loops. In this model, a quantum state ∣ψ⟩|\psi\rangle∣ψ⟩ interacts unitarily with its past version, effectively forming a two-qubit system where the chronologically consistent qubit interacts with a qubit ρCTC\rho_{\text{CTC}}ρCTC trapped in a closed timelike curve. The state ρCTC\rho_{\text{CTC}}ρCTC is determined by the Deutsch consistency condition, ensuring self-consistent evolution along the CTC. This approach allows for rigorous modeling of quantum systems under non-classical temporal structures, providing insights into temporal correlations, causality violations, and the potential computational advantages offered by CTC-assisted quantum operations. While alternative CTC models based on postselection have been proposed, the Deutsch model remains a foundational reference for studying quantum evolution in non-linear temporal frameworks. Its analysis informs research in quantum information, retrocausality, and the theoretical limits of computation in exotic spacetime geometries.
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D 44, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP\mathit{NP}NP-complete problems with only a polynomial number of quantum gates.
The possibility of performing quantum cloning in the presence of closed time like curves is considered. We analyze a model of the quantum cloning process involving a source qubit, a target qubit, and a quantum copy machine which is itself a composite quantum system. A subsystem of the copy machine is allowed to traverse a closed time like curve. Under these circumstances the evolution of the chronology respecting parts of the system is nonlinear. This suggests (Deutsch, 1991) that quantum cloning might be possible. We prove that, if only one subsystem of the copy machine is allowed to traverse a closed time like curve and the copy machine’s Hilbert space is of finite dimension, universal quantum cloning is impossible.
Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.
Many results have been recently obtained regarding the power of hypothetical closed timelike curves (CTCs) in quantum computation. Here we show that the one-way model of measurement-based quantum computation encompasses in a natural way the CTC model proposed by Bennett, Schumacher, and Svetlichny. We identify a class of CTCs in this model that can be simulated deterministically and point to a fundamental limitation of Deutsch's CTC model which leads to predictions conflicting with those of the one-way model.