Post-Markovian quantum master equations from classical environment fluctuations

Abstract

In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its associated approximated integro-differential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unravelled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

13 pages, 4 figures

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• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Maximally non-Markovian quantum dynamics without environment backflow of information
• A generic map from non-Lindblad to Lindblad master equations
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Quantum renewal processes
• Non-Markovianity of the Post Markovian Master Equation
• Detection of Bidirectional System-Environment Information Exchanges
• A solvable class of non-Markovian quantum multipartite dynamics
• Minimalistic analytical approach to non-Markovian open quantum systems