Bounds for the divisibility-based and distinguishability-based non-Markovianity measures

Abstract

We derive an upper bound for the distinguishability-based non-Markovianity measure of a two-level system and prove that for certain master equations the exact value of the measure achieves this bound. Furthermore, we obtain an easily calculable lower bound for the divisibility-based non-Markovianity measure of an $n$-level system. We illustrate the calculation of these bounds through examples, considering in detail the spin-boson model. We show that the differences between the two measures in the spin-boson model are caused by the drift vector that is also responsible for the non-unitality of the dynamical map.

arXiv comment8 pages, one figure. v2: Typos corrected, one reference added

References in corpus (20)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Measure for the Non-Markovianity of Quantum Processes
• Canonical form of master equations and characterization of non-Markovianity
• On the degree of non-Markovianity of quantum evolution
• Dividing Quantum Channels
• On measures of non-Markovianity: divisibility vs. backflow of information
• Geometrical characterization of non-Markovianity
• Markovian and non-Markovian dynamics in quantum and classical systems
• Optimal state pairs for non-Markovian quantum dynamics
• Comparing different non-Markovianity measures: A case study
• Quantum regression theorem and non-Markovianity of quantum dynamics
• Quantification of memory effects in the spin-boson model
• An effective method of calculating the non-Markovianity $\mathcal{N}$ for single channel open systems
• Non-unital non-Markovianity of quantum dynamics
• Parametrizations of density matrices
• Effects of the rotating wave and secular approximations on non-Markovianity
• Non-Markovian dynamics for an open two-level system without rotating wave approximation: Indivisibility versus backflow of information

Cited by in corpus (2)

• Eternal non-Markovianity is generic for the spin-boson model
• Exact Non-Markovian master equation for the Spin-Boson and Jaynes-Cummings models