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Quantum trajectory framework for general time-local master equations

Author

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  • Brecht Donvil

    (University of Helsinki, Department of Mathematics and Statistics
    Ulm University)

  • Paolo Muratore-Ginanneschi

    (University of Helsinki, Department of Mathematics and Statistics)

Abstract

Master 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.

Suggested Citation

  • Brecht Donvil & Paolo Muratore-Ginanneschi, 2022. "Quantum trajectory framework for general time-local master equations," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-31533-8
    DOI: 10.1038/s41467-022-31533-8
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    1. Z. K. Minev & S. O. Mundhada & S. Shankar & P. Reinhold & R. Gutiérrez-Jáuregui & R. J. Schoelkopf & M. Mirrahimi & H. J. Carmichael & M. H. Devoret, 2019. "To catch and reverse a quantum jump mid-flight," Nature, Nature, vol. 570(7760), pages 200-204, June.
    2. Barchielli, A. & Holevo, A. S., 1995. "Constructing quantum measurement processes via classical stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 293-317, August.
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