Completely positive maps with memory

Abstract

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.

4 pages

References in corpus (2)

• Quantum Markov Channels for Qubits
• Restriction on relaxation times derived from the Lindblad-type master equations for 2-level systems

Cited by in corpus (121)

• Finite-Time Disentanglement via Spontaneous Emission
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum speed limits in open system dynamics
• Measure for the Non-Markovianity of Quantum Processes
• Quantum channels and memory effects
• On measures of non-Markovianity: divisibility vs. backflow of information
• Non-Markovian quantum dynamics: local versus non-local
• Quantum Channels with Memory
• Non-Markovian dynamics of a qubit
• Markovian and non-Markovian dynamics in quantum and classical systems
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Collision-model-based approach to non-Markovian quantum dynamics
• Exact master equations for the non-Markovian decay of a qubit
• Witness for initial system-environment correlations in open system dynamics
• Measuring non-Markovianity of processes with controllable system-environment interaction
• Initial correlations in open system's dynamics: The Jaynes-Cummings model
• Quantum Semi-Markov Processes
• Comparing different non-Markovianity measures: A case study
• Non-Markovian random unitary qubit dynamics
• Dynamics of quantum correlations in colored environments
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Completely positive master equation for arbitrary driving and small level spacing
• Hierarchy and dynamics of trace distance correlations
• Staying positive: going beyond Lindblad with perturbative master equations
• Structure of completely positive quantum master equations with memory kernel
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• Frozen discord in non-Markovian dephasing channels
• Lindblad rate equations
• Non-Markovian behavior of small and large complex quantum systems
• Random Lindblad equations from complex environments
• Phenomenological memory-kernel master equations and time-dependent Markovian processes
• Generalized master equations leading to completely positive dynamics
• An effective method of calculating the non-Markovianity $\mathcal{N}$ for single channel open systems
• Non-Markovian evolution: a quantum walk perspective
• Non-Markovian quantum input-output networks
• Sudden change of quantum discord for a system of two qubits
• Non-Markovian dephasing and depolarizing channels
• Tomographically reconstructed master equations for any open quantum dynamics
• Markovianity criteria for quantum evolution
• Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
• Dynamical Memory Effects in Correlated Quantum Channels
• Necessary and sufficient conditions of freezing phenomena of quantum discord under phase damping
• Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
• Facets of quantum information under non-Markovian evolution
• Conservative chaotic map as a model of quantum many-body environment
• Entanglement evolution of two qubits under noisy environments
• Markovian embedding of non-Markovian quantum collisional models
• Quantum cryptography over non-Markovian channels
• Controlling entropic uncertainty bound through memory effects
• On admissible memory kernels for random unitary qubit evolution
• Non-Markovian non-stationary completely positive open quantum system dynamics
• Open system dynamics from thermodynamic compatibility
• Estimating the degree of non-Markovianity using machine learning
• On the indistinguishability of Raman photons
• The interplay between local and non-local master equations: exact and approximated dynamics
• Dynamics of genuine multipartite entanglement under local non-Markovian dephasing
• Singularity of dynamical maps
• Non-Markovian master equations from entanglement with stationary unobserved degrees of freedom
• Quantum thermo-dynamical construction for driven open quantum systems
• Noise suppression via generalized-Markovian processes
• Quantum regression theorem for non-Markovian Lindblad equations
• Witnessing non-Markovianity of quantum evolution
• Hierarchy of quantum correlations under non-Markovian dynamics
• Constructive Feedback of Non-Markovianity on Resources in Random Quantum States
• Inequivalence of Correlation-based Measures of Non-Markovianity
• Post-Markovian quantum master equations from classical environment fluctuations
• Non-Markovian channel from the reduced dynamics of coin in quantum walk
• Quantum-circuit guide to optical and atomic interferometry
• Recursive approach for non-Markovian time-convolutionless master equations
• Relaxation times in an open interacting two-qubit system
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
• Exploring initial correlations in a Gibbs state by local application of external field
• Non-Markovian Quantum Dynamics and Classical Chaos
• Quantum Correlations Dynamics In Two Coupled Semiconductor InAs Quantum Dots
• Quantum renewal processes
• Characterizing qubit channels in the context of quantum teleportation
• Reduced Dynamics of Full Counting Statistics
• Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels
• Memory effect on the bidirectional teleportation
• Conditions for the freezing phenomena of geometric measure of quantum discord for arbitrary two-qubit X states under non-dissipative dephasing noises
• Quantumness of gravitational cat states in correlated dephasing channels
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Classical memoryless noise-induced maximally discordant mixed separable steady states
• Kernel-based quantum regressor models learn non-Markovianity
• Attainable and usable coherence in X states over Markovian and non-Markovian channels
• Measure of not-completely-positive qubit maps: the general case
• Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps
• Correlation dynamics of a two-qubit system in a Bell-diagonal state under non-identical local noises
• A study of coherence based measure of quantumness in (non) Markovian channels
• A solvable class of non-Markovian quantum multipartite dynamics
• Protecting quantum correlations of negative quantum states using weak measurement under non-Markovian noise
• Interplay between nonclassicality and $\mathcal{P}\mathcal{T}$ symmetry in an effective two level system with open system effects
• Quantumness of channels
• On the standard quantum Brownian equation and an associated class of non-autonomous master equations
• Master Equation Emulation and Coherence Preservation with Classical Control of a Superconducting Qubit
• Connecting two jumplike unravelings for non-Markovian open quantum systems
• Facets of correlated non-Markovian channels
• Quantifying non-Markovianity via local quantum Fisher information
• Memory effects in quantum dynamics modelled by quantum renewal processes
• Non-Markovian Equilibration Controlled by Symmetry Breaking
• Quantum non-Markovian behavior at the chaos border
• Superiority in dense coding through non-Markovian stochasticity
• Non-Markovian memory in a measurement-based quantum computer
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Noise-adapted Quantum Error Correction for Non-Markovian Noise
• Localizing genuine multiparty entanglement in noisy stabilizer states
• Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed
• Frozen and Invariant Quantum Discord under Local Dephasing Noise
• Superclassical non-Markovian open quantum dynamics
• Distinguishing environment-induced non-Markovianity from subsystem dynamics
• Entanglement may enhance the channel capacity in arbitrary dimensions
• Decoherence of Dirac-particle quantumness for fermionic fields in a dilatonic black hole
• Invariance of success probability in Grover's quantum search under local noise with memory
• The classical capacity for the quantum Markov channel of continuous variables
• Sudden change of interferometric power for X shape states
• Estimating the degree of non-Markovianity using variational quantum circuits
• Projective measurements under qubit quantum channels
• Finite-Bath Open Quantum Systems: Exact Dynamics
• Field mixing in a thermal medium: A quantum master equation approach