On generalized semi-Markov quantum evolution

Abstract

We provide a large class of quantum evolution governed by the memory kernel master equation. This class defines quantum analog of so called semi-Markov classical stochastic evolution. In this Letter for the first time we provide a proper definition of quantum semi-Markov evolution and using the appropriate gauge freedom we propose a suitable generalization which contains majority of examples considered so far in the literature. The key concepts are quantum counterparts of classical waiting time distribution and survival probability -- quantum waiting time operator and quantum survival operator, respectively. In particular collision models and its generalizations considered recently are special examples of generalized semi-Markov evolution. This approach allows for an interesting generalization of trajectory description of the quantum dynamics in terms of POVM densities.

6 pages

References in corpus (10)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Collision-model-based approach to non-Markovian quantum dynamics
• Quantum Semi-Markov Processes
• Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
• Structure of completely positive quantum master equations with memory kernel
• Generalized master equations leading to completely positive dynamics
• Sufficient conditions for memory kernel master equation
• Class of exact memory-kernel master equations
• General structure of quantum collisional models

Cited by in corpus (23)

• Quantum collision models: open system dynamics from repeated interactions
• Composite quantum collision models
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Phase covariant qubit dynamics and divisibility
• Quantum non-Markovian piecewise dynamics from collision models
• Rate operator unravelling for open quantum system dynamics
• Memory kernel approach to generalized Pauli channels: Markovian, semi-Markov, and beyond
• Noise suppression via generalized-Markovian processes
• Convex combinations of CP-divisible Pauli channels that are not semigroups
• How quantum evolution with memory is generated in a time-local way
• Time deformations of master equations
• Quantum renewal processes
• Markovian semigroup from mixing non-invertible dynamical maps
• The connection between time-local and time-nonlocal perturbation expansions
• Engineering fidelity of the generalized Pauli channels via legitimate memory kernels
• Invertibility as a witness of Markovianity of the quantum dynamical maps
• Microscopic modelling of general time-dependent quantum Markov processes
• A solvable class of non-Markovian quantum multipartite dynamics
• Engineering classical capacity of generalized Pauli channels with admissible memory kernels
• Master Equation Emulation and Coherence Preservation with Classical Control of a Superconducting Qubit
• Two definitions of the Gell-Mann channels - a comparative analysis
• Improving classical capacity of qubit dynamical maps through stationary state manipulation
• Frontiers of open quantum system dynamics