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 (12)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Entanglement and non-Markovianity of quantum evolutions
• Open Quantum Systems. An Introduction
• Assessing non-Markovian dynamics
• Measure for the Non-Markovianity of Quantum Processes
• Foundations and Measures of Quantum Non-Markovianity
• Collision-model-based approach to non-Markovian quantum dynamics
• Simulation of indivisible qubit channels in collision models
• Non-Markovian master equations from piecewise dynamics
• Markovian embedding of non-Markovian quantum collisional models
• Master equation for cascade quantum channels: a collisional approach
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics

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• Collision models in open system dynamics: A versatile tool for deeper insights?
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• Sufficient conditions for memory kernel master equation
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• Quantum synchronization in a collision model
• Synchronization and Non-Markovianity in open quantum systems
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• Quantum non-Markovian piecewise dynamics from collision models
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• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• A brief journey through collision models for multipartite open quantum dynamics
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• Non-Markovian open dynamics from collision models
• Frontiers of open quantum system dynamics
• Witnessing Objectivity on a Quantum Computer
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• All-optical implementation of collision-based evolutions of open quantum systems
• Stabilization and Dissipative Information Transfer of a Superconducting Kerr-Cat Qubit