International Journal of Theoretical Physics

, Volume 42, Issue 9, pp 2025–2041 | Cite as

Discrete Quantum Causal Dynamics

  • Richard F. Blute
  • Ivan T. Ivanov
  • Prakash Panangaden


We give a mathematical framework to describe the evolution of open quantum systems subject to finitely many interactions with classical apparatuses and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. This evolution, driven both by unitary operators and measurements, is coded in a mathematical structure in such a way that the crucial properties of causality, covariance, and entanglement are faithfully represented. The key to this scheme is the use of a special family of spacelike slices—we call them locative—that are not so large as to result in acausal influences but large enough to capture nonlocal correlations.

discrete quantum systems causality entanglement 


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  1. Blencowe, M. (1991). The consistent histories interpretation of quantum fields in curved space-time. Annals of Physics 211, 87-111.Google Scholar
  2. Bombelli, L., Lee, J., Meyer, D., and Sorkin, R. (1987). Spacetime as a causal set. Physical Review Letters 59, 521-524.Google Scholar
  3. Davies, E. B. (1976). Quantum Theory of Open Systems, Academic Press, New York.Google Scholar
  4. Gell-Mann, M. and Hartle, J. B. (1993). Classical equations for quantum systems. Physical Review D: Particles and Fields 47, 3345-3382.Google Scholar
  5. Griffiths, R. B. (1996). Consistent histories and quantum reasoning. Physical Review A 54, 2759-2774.Google Scholar
  6. Markopoulou, F. (2000). Quantum causal histories. Classical and Quantum Gravity 17, 2059-2077.Google Scholar
  7. Markopoulou, F. and Smolin, L. (1997). Causal evolution of spin networks. Nuclear Physics B 508, 409-430.Google Scholar
  8. Nielsen, M. and Chuang, I. (2000). Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK.Google Scholar
  9. Omnès, R. (1994). The Interpretation of Quantum Mechanics, Princeton University Press, Princeton, NJ.Google Scholar
  10. Peres, A. (1995). Quantum Theory: Concepts and Methods, Kluwer Academic, Norwell, MA.Google Scholar
  11. Peres, A. (2000a). Classical interventions in quantum systems: I. The measuring process. Physical Review A 61, 022116.Google Scholar
  12. Peres, A. (2000b). Classical interventions in quantum systems: II. Relativistic invariance. Physical Review A 61, 022117.Google Scholar
  13. Plotkin, G. D. (1976). A powerdomain construction. SIAM Journal of Computing 5(3), 452-487.Google Scholar
  14. Penrose, R. and MacCallum, M. A. H. (1972). Twistor theory: An approach to the quantization of fields and spacetime. Physics Reports 6C, 241-315.Google Scholar
  15. Preskill, J. Quantum Information and Computation. Lecture Notes, California Institute of Technology, CA.Google Scholar
  16. Raptis, I. (2000). Finitary spacetime sheaves. International Journal of Theoretical Physics 39, 1703-1720.Google Scholar
  17. Sorkin, R. (1991). Spacetime and causal sets. I. Relativity and Gravitation: Classical and Quantum, J. D'Olivo et al., ed., World Scientific, SingaporeGoogle Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Richard F. Blute
    • 1
  • Ivan T. Ivanov
    • 1
  • Prakash Panangaden
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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