Abstract
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.
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References
Blencowe, M. (1991). The consistent histories interpretation of quantum fields in curved space-time. Annals of Physics 211, 87-111.
Bombelli, L., Lee, J., Meyer, D., and Sorkin, R. (1987). Spacetime as a causal set. Physical Review Letters 59, 521-524.
Davies, E. B. (1976). Quantum Theory of Open Systems, Academic Press, New York.
Gell-Mann, M. and Hartle, J. B. (1993). Classical equations for quantum systems. Physical Review D: Particles and Fields 47, 3345-3382.
Griffiths, R. B. (1996). Consistent histories and quantum reasoning. Physical Review A 54, 2759-2774.
Markopoulou, F. (2000). Quantum causal histories. Classical and Quantum Gravity 17, 2059-2077.
Markopoulou, F. and Smolin, L. (1997). Causal evolution of spin networks. Nuclear Physics B 508, 409-430.
Nielsen, M. and Chuang, I. (2000). Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK.
Omnès, R. (1994). The Interpretation of Quantum Mechanics, Princeton University Press, Princeton, NJ.
Peres, A. (1995). Quantum Theory: Concepts and Methods, Kluwer Academic, Norwell, MA.
Peres, A. (2000a). Classical interventions in quantum systems: I. The measuring process. Physical Review A 61, 022116.
Peres, A. (2000b). Classical interventions in quantum systems: II. Relativistic invariance. Physical Review A 61, 022117.
Plotkin, G. D. (1976). A powerdomain construction. SIAM Journal of Computing 5(3), 452-487.
Penrose, R. and MacCallum, M. A. H. (1972). Twistor theory: An approach to the quantization of fields and spacetime. Physics Reports 6C, 241-315.
Preskill, J. Quantum Information and Computation. Lecture Notes, California Institute of Technology, CA.
Raptis, I. (2000). Finitary spacetime sheaves. International Journal of Theoretical Physics 39, 1703-1720.
Sorkin, R. (1991). Spacetime and causal sets. I. Relativity and Gravitation: Classical and Quantum, J. D'Olivo et al., ed., World Scientific, Singapore
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Blute, R.F., Ivanov, I.T. & Panangaden, P. Discrete Quantum Causal Dynamics. International Journal of Theoretical Physics 42, 2025–2041 (2003). https://doi.org/10.1023/A:1027335119549
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DOI: https://doi.org/10.1023/A:1027335119549