General structure of quantum collisional models

Abstract

We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time dependent completely positive maps, a completely positive trace preserving transformation and a waiting time distribution characterizing a renewal process. The relationship between this construction and a Lindblad dynamics is clarified by expressing the solution of a Lindblad master equation in terms of demixtures over different stochastic trajectories for the statistical operator weighted by suitable probabilities on the trajectory space.

9 pages, 1 figure; proceedings of the conference IQIS 2013 to appear on IJQI

References in corpus (4)

• Assessing non-Markovian dynamics
• Foundations and Measures of Quantum Non-Markovianity
• Collision-model-based approach to non-Markovian quantum dynamics
• Simulation of indivisible qubit channels in collision models

Cited by in corpus (5)

• Composite quantum collision models
• Generalized master equations leading to completely positive dynamics
• Quantum non-Markovian piecewise dynamics from collision models
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Frontiers of open quantum system dynamics