Foundations of Physics

, Volume 47, Issue 3, pp 375–391 | Cite as

Simulations of Closed Timelike Curves

  • Todd A. Brun
  • Mark M. WildeEmail author


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.


Closed timelike curves Teleportation Simulation PSPACE Deutschian CTCs Postselected CTCs Transition probability CTCs 



We are especially grateful to Tom Cooney for many enlightening discussions on fixed points of CPTP linear maps. We thank John-Mark Allen for helpful feedback that improved the manuscript. We also acknowledge Jonathan Dowling for his help in obtaining FQXI funds to support this research. Finally, we acknowledge support from the Department of Physics and Astronomy at Louisiana State University and the Foundational Questions Institute (FQXI) for supporting the grant “Closed timelike curves and quantum information processing.”


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Ming Hsieh Department of Electrical Engineering, Center for Quantum Information Science and TechnologyUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Physics and AstronomyHearne Institute for Theoretical Physics, Center for Computation and Technology, Louisiana State UniversityBaton RougeUSA

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