Abstract
AbstractMaster equations are one of the main avenues to study open quantum systems. When the master equation is of the Lindblad–Gorini–Kossakowski–Sudarshan form, its solution can be “unraveled in quantum trajectories” i.e., represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces. We prove that general time-local and trace-preserving master equations also admit an unraveling in terms of a Markov process in the Hilbert space of the system. The crucial ingredient is to weigh averages by a probability pseudo-measure which we call the “influence martingale”. The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. We thus extend the existing theory without increasing the computational complexity.
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Biochemistry, Genetics and Molecular Biology,General Chemistry,Multidisciplinary
Reference70 articles.
1. Haroche, S. & Raimond, J.-M. Exploring the Quantum: Atoms, Cavities, and Photons X, 616 (Oxford Graduate Texts, 2006).
2. Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems reprint edn XXII, 636 (Oxford University Press, 2002).
3. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control 1st edn 478 (Cambridge University Press, 2009).
4. Sauter, T. H., Neuhauser, W., Blatt, R. & Toschek, P. E. Observation of quantum jumps. Phys. Rev. Lett. 57, 1696–1698 (1986).
5. Bergquist, J. C., Hulet, R. G., Itano, W. M. & Wineland, D. J. Observation of quantum jumps in a single atom. Phys. Rev. Lett. 57, 1699–1702 (1986).
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