Tomographically reconstructed master equations for any open quantum dynamics

Felix A. Pollock and Kavan Modi

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.

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Cited by

[1] Shlok Nahar and Sai Vinjanampathy, "Preparations and Weak Quantum Control can Witness non-Markovianity", arXiv:1803.08443 (2018).

[2] Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, and Kavan Modi, "Non-Markovian quantum processes: Complete framework and efficient characterization", Physical Review A 97 1, 012127 (2018).

[3] Leonardo Banchi, Edward Grant, Andrea Rocchetto, and Simone Severini, "Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks", New Journal of Physics 20 12, 123030 arXiv:1808.01374 (2018).

[4] Simon Milz, Felix A. Pollock, and Kavan Modi, "An Introduction to Operational Quantum Dynamics", Open Systems and Information Dynamics 24 4, 1740016 (2017).

[5] Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, and Kavan Modi, "Non-Markovian quantum processes: complete framework and efficient characterisation", arXiv:1512.00589 (2015).

[6] Maximilian Buser, Javier Cerrillo, Gernot Schaller, and Jianshu Cao, "Initial system-environment correlations via the transfer-tensor method", Physical Review A 96 6, 062122 (2017).

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