Quantum renewal processes
arXiv:1906.00693 · doi:10.1038/s41598-020-62260-z
Abstract
We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical renewal processes, so that they are termed quantum renewal processes. They can be described by means of semigroup dynamics interrupted by jumps, separated by independently distributed time intervals, following suitable waiting time distributions. In this framework, one can further introduce modified processes, in which the first few events follow different distributions. A crucial role, marking an important difference with respect to the classical case, is played by operator ordering. Indeed, for the same choice of basic quantum transformations, different quantum dynamics arise. In particular, for the case of modified processes, it is natural to consider the time inverted operator ordering, in which the last few events are distributed differently.
arXiv comment23 pages, 6 figures
References in corpus (44)
- Non-Markovian dynamics in open quantum systems
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Open Quantum Systems. An Introduction
- Concepts and methods in the theory of open quantum systems
- Canonical form of master equations and characterization of non-Markovianity
- Non-Markovian quantum dynamics: local versus non-local
- Foundations and Measures of Quantum Non-Markovianity
- Completely positive maps with memory
- Completely Positive Post-Markovian Master Equation via a Measurement Approach
- Collision-model-based approach to non-Markovian quantum dynamics
- Master equations for correlated quantum channels
- Quantum Semi-Markov Processes
- Collision model for non-Markovian quantum dynamics
- Collisional quantum thermometry
- Experimental observation of weak non-Markovianity
- Non-Markovianity and System-Environment Correlations in a microscopic collision model
- Simulation of indivisible qubit channels in collision models
- Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
- System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
- Nakajima-Zwanzig versus time-convolutionless master equation for the non-Markovian dynamics of a two-level system
- Structure of completely positive quantum master equations with memory kernel
- Random Lindblad equations from complex environments
- Generalized master equations leading to completely positive dynamics
- Non-Markovianity, coherence and system-environment correlations in a long-range collision model
- Non-Markovian master equations from piecewise dynamics
- Sufficient conditions for memory kernel master equation
- Class of exact memory-kernel master equations
- Five Lectures On Dissipative Master Equations
- Robust multipartite entanglement generation via a collision model
- Non-Markovianity in a collision model with environmental block
- Collisional unfolding of quantum Darwinism
- Mixing-induced quantum non-Markovianity and information flow
- Master equation for cascade quantum channels: a collisional approach
- On generalized semi-Markov quantum evolution
- Non-Markovian non-stationary completely positive open quantum system dynamics
- Quantum non-Markovian piecewise dynamics from collision models
- Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
- On time-local generators of quantum evolution
- Critical assessment of two-qubit post-Markovian master equations
- Post-Markovian quantum master equations from classical environment fluctuations
- Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
- Multiple-scale analysis of open quantum systems
- Microscopic modelling of general time-dependent quantum Markov processes
- Non-Markovian open dynamics from collision models
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- Evolution equations for quantum semi-Markov dynamics
- Memory effects in quantum dynamics modelled by quantum renewal processes
- Parameter estimation for quantum jump unraveling
- Queued quantum collision models
- Witnessing Objectivity on a Quantum Computer