Tomographically reconstructed master equations for any open quantum dynamics

Abstract

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.

10+4 pages, 5 figures

References in corpus (12)

• Many body localization and thermalization in quantum statistical mechanics
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Quantum Zeno dynamics: mathematical and physical aspects
• Operational Markov condition for quantum processes
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Quantum Semi-Markov Processes
• Generalized master equations leading to completely positive dynamics
• Characterizing quantum dynamics with initial system-environment correlations
• Initial System-Environment Correlations via the Transfer Tensor Method
• Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models
• A tomographic approach to non-Markovian master equations
• Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

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