Non-Markovianity and memory effects in quantum open systems

Abstract

Although a number of measures for quantum non-Markovianity have been proposed recently, it is still an open question whether these measures directly characterize the memory effect of the environment, i.e., the dependence of a quantum state on its past in a time evolution. In this paper, we present a criterion and propose a measure for non-Markovianity with clear physical interpretations of the memory effect. The non-Markovianity is defined by the inequality $T(t_2,t_0)\ne T(t_2,t_1)T(t_1,t_0)$ in terms of memoryless dynamical map $T$ introduced in this paper. This definition is conceptually distinct from that based on divisibility used by Rivas et al (Phys. Rev. Lett 105, 050403 (2010)), whose violation is manifested by non-complete positivity of the dynamical map. We demonstrate via a typical quantum process that without Markovian approximation, nonzero memory effects (non-Markovianity) always exist even if the non-Markovianity is zero by the other non-Marovianity measures.

9 pages, 4 figures

References in corpus (34)

• 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
• Open Quantum Systems. An Introduction
• Distance measures to compare real and ideal quantum processes
• Quantum Metrology in Non-Markovian Environments
• Assessing non-Markovian dynamics
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Quantum speed limit for non-Markovian dynamics
• Measure for the Non-Markovianity of Quantum Processes
• Non-Markovian Dynamics of Quantum Discord
• Canonical form of master equations and characterization of non-Markovianity
• On the degree of non-Markovianity of quantum evolution
• General non-Markovian dynamics of open quantum systems
• Geometrical characterization of non-Markovianity
• Non-Markovian quantum dynamics: local versus non-local
• Foundations and Measures of Quantum Non-Markovianity
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Non-Markovianity assisted Steady State Entanglement
• Experimental demonstration of photonic entanglement collapse and revival
• Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity
• Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
• Quantifying non-Markovianity of continuous variable Gaussian dynamical maps
• Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
• An alternative non-Markovianity measure by divisibility of dynamical map
• Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain
• A fidelity measure for quantum channels
• Non-unital non-Markovianity of quantum dynamics
• Oscillatory dynamics and non-markovian memory in dissipative quantum systems
• Quantum discord and non-Markovianity of quantum dynamics
• Continuous Measurement of a Non-Markovian Open Quantum System
• Singularity of dynamical maps
• Quantum Gate Fidelity in Terms of Choi Matrices

Cited by in corpus (12)

• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Non-Markovianity in a collision model with environmental block
• Non-Markovian continuous-time quantum walks on lattices with dynamical noise
• Optomechanical quadrature squeezing in the non-Markovian regime
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics
• Maximally non-Markovian quantum dynamics without environment backflow of information
• Multiple single-photon generations in three-level atoms coupled to cavity with non-Markovian effects
• Non-Markovian Dynamics in Ultracold Rydberg Aggregates
• Non-Markovianity is not a resource for quantum spatial search on a star graph subject to generalized percolation
• Influence of initial states on memory effects: A study of early-time superradiance
• Non-Markovian dynamics for a two-atom-coupled system interacting with local reservoir at finite temperature
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems