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

AIP conference proceedings

Would Closed Timelike Curves Help to Do Quantum Cloning?

Angel Ricardo Plastino

Published Jan 1, 2006• 5 citations
Publisher

Abstract

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.

DOI
10.1063/1.2218239

Related papers

Any quantum state can be cloned in the presence of closed timelike curves

Doyeol Ahn, Timothy C. Ralph, Mann, R. B.

The possible existence of closed timelike curves (CTCs) draws attention to fundamental questions about what is physically possible and what is not. An example is the "no cloning theorem" in quantum mechanics, which states that no physical means exists by which an unknown arbitrary quantum state can be reproduced or copied perfectly. Using the Deutsch approach, we show here that this theorem can be circumvented in the presence of closed timelike curves, allowing the cloning of an unknown arbitrary quantum state chosen from a finite alphabet of states. Since the "no cloning theorem" has played a central role in the development of quantum information science, it is clear that the existence of CTCs would radically change the rules for quantum information technology. Nevertheless we show that this type of cloning does not violate no-signalling criteria.

arXiv:1008.0221•Aug 2, 2010•3 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

Quantum State Cloning Using Deutschian Closed Timelike Curves

Todd A. Brun, Mark M. Wilde, Andreas Winter

We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large--thus resolving an open conjecture [Brun et al., Phys. Rev. Lett. 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme for producing perfect clones of a quantum state prepared in a known eigenbasis, and the fact that one can reconstruct an approximation of a quantum state from empirical estimates of the probabilities of an informationally complete measurement. Our results imply more generally that every continuous, but otherwise arbitrarily nonlinear map from states to states, can be implemented to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch's model for closed timelike curves is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large closed timelike curve system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space.

arXiv:1306.1795•Physical Review Letters•Nov 4, 2013•35 citations

Quantum-state cloning in the presence of a closed timelike curve

Doyeol Ahn, Casey R. Myers, Timothy C. Ralph +1 more

Using the Deutsch model of closed timelike curves, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the no-cloning bound for fidelity. Since the no-cloning theorem has played a central role in the development of quantum information science, it is clear that the existence of closed timelike curves that behave according to Deutsch's model would radically change the rules for quantum information technology. Nevertheless, we show that this type of cloning does not violate no-signaling criteria.

arXiv:1207.6062•Physical Review A•Aug 26, 2013•32 citations

Closed time like curves enable perfect state distinguishability

James William Harrington, Mark M. Wilde, Todd A. Brun

The causal self-consistency condition for closed timelike curves can give rise to nonlinear interactions on chronology-respecting qubits. We demonstrate that particular unitary interactions between closed timelike curve qubits and chronology-respecting qubits allow perfect distinguishability of nonorthogonal states, and provide a constructive proof for an arbitrary number of nonorthogonal states. This has a number of highly significant consequences. For example, an adversary with access to closed timelike curves can break the B92, BB84, and SARG04 quantum key distribution protocols, or any prepare-and-measure quantum key distribution scheme. Our result also implies that a party with access to closed timelike curves can violate the Holevo bound by accessing more than log(N) bits of information from an N-dimensional quantum state. In principle, he can transmit an arbitrarily large amount of classical information with a quantum system of fixed size. We discuss the implications of this for quantum cloning.

•Jan 1, 2008•0 citations

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
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.
The possible existence of closed timelike curves (CTCs) draws attention to fundamental questions about what is physically possible and what is not. An example is the "no cloning theorem" in quantum mechanics, which states that no physical means exists by which an unknown arbitrary quantum state can be reproduced or copied perfectly. Using the Deutsch approach, we show here that this theorem can be circumvented in the presence of closed timelike curves, allowing the cloning of an unknown arbitrary quantum state chosen from a finite alphabet of states. Since the "no cloning theorem" has played a central role in the development of quantum information science, it is clear that the existence of CTCs would radically change the rules for quantum information technology. Nevertheless we show that this type of cloning does not violate no-signalling criteria.
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.
We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large--thus resolving an open conjecture [Brun et al., Phys. Rev. Lett. 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme for producing perfect clones of a quantum state prepared in a known eigenbasis, and the fact that one can reconstruct an approximation of a quantum state from empirical estimates of the probabilities of an informationally complete measurement. Our results imply more generally that every continuous, but otherwise arbitrarily nonlinear map from states to states, can be implemented to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch's model for closed timelike curves is in fact a classical model, in the sense that two arbitrary, distinct density operators are perfectly distinguishable (in the limit of a large closed timelike curve system); hence, in this model quantum mechanics becomes a classical theory in which each density operator is a distinct point in a classical phase space.
Using the Deutsch model of closed timelike curves, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the no-cloning bound for fidelity. Since the no-cloning theorem has played a central role in the development of quantum information science, it is clear that the existence of closed timelike curves that behave according to Deutsch's model would radically change the rules for quantum information technology. Nevertheless, we show that this type of cloning does not violate no-signaling criteria.
The causal self-consistency condition for closed timelike curves can give rise to nonlinear interactions on chronology-respecting qubits. We demonstrate that particular unitary interactions between closed timelike curve qubits and chronology-respecting qubits allow perfect distinguishability of nonorthogonal states, and provide a constructive proof for an arbitrary number of nonorthogonal states. This has a number of highly significant consequences. For example, an adversary with access to closed timelike curves can break the B92, BB84, and SARG04 quantum key distribution protocols, or any prepare-and-measure quantum key distribution scheme. Our result also implies that a party with access to closed timelike curves can violate the Holevo bound by accessing more than log(N) bits of information from an N-dimensional quantum state. In principle, he can transmit an arbitrarily large amount of classical information with a quantum system of fixed size. We discuss the implications of this for quantum cloning.
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.