Non-Markovian random unitary qubit dynamics

Abstract

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates. As a byproduct it is shown that entropy might monotonically increase even for non-Markovian qubit dynamics.

5 pages

References in corpus (29)

• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Entanglement and non-Markovianity of quantum evolutions
• 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
• Non-Markovian Quantum State Diffusion
• Open system dynamics with non-Markovian quantum trajectories
• Non-Markovian quantum jumps
• Dividing Quantum Channels
• On measures of non-Markovianity: divisibility vs. backflow of information
• Non-Markovian quantum dynamics: local versus non-local
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Completely positive maps with memory
• Non-Markovian dynamics of a qubit
• Revival of quantum correlations without system-environment back-action
• Markovian and non-Markovian dynamics in quantum and classical systems
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Open system dynamics with non-Markovian quantum jumps
• Quantum Semi-Markov Processes
• Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
• Comparing different non-Markovianity measures: A case study
• 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
• Structure of completely positive quantum master equations with memory kernel
• Markovianity criteria for quantum evolution
• A classical appraisal of quantum definitions of non-Markovian dynamics
• Limits in the characteristic function description of non-Lindblad-type open quantum systems
• Singularity of dynamical maps
• Comparison of non-Markovianity criteria in a qubit system under random external fields

Cited by in corpus (63)

• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Canonical form of master equations and characterization of non-Markovianity
• On the degree of non-Markovianity of quantum evolution
• Generalized trace distance measure connecting quantum and classical non-Markovianity
• Non-Markovianity degree for random unitary evolution
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Adding dynamical generators in quantum master equations
• Generalized Pauli channels and a class of non-Markovian quantum evolution
• Role of non-Markovianity and backflow of information in the speed of quantum evolution
• Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed
• There is no general connection between the quantum speed limit and non-Markovianity
• Experimental investigation of the effect of classical noise on quantum non-Markovian dynamics
• Mixing-induced quantum non-Markovianity and information flow
• On admissible memory kernels for random unitary qubit evolution
• Tensor power of dynamical maps and P- vs. CP-divisibility
• Rate operator unravelling for open quantum system dynamics
• The interplay between local and non-local master equations: exact and approximated dynamics
• Entanglement negativity as a universal non-Markovianity witness
• A correlation measure detecting almost all non-Markovian evolutions
• On time-local generators of quantum evolution
• Hierarchy of Non-Markovianity and $k$-divisibility phase diagram of Quantum Processes in Open Systems
• Classical capacity of the generalized Pauli channels
• Maximally non-Markovian quantum dynamics without environment backflow of information
• Witnessing non-Markovianity of quantum evolution
• Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
• Witnessing non-Markovian dynamics through correlations
• Dissipative generators, divisible dynamical maps and Kadison-Schwarz inequality
• Entanglement generation between a charge qubit and its bosonic environment during pure dephasing - dependence on environment size
• Local disclosure of quantum memory in non-Markovian dynamics
• Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility
• Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• On pseudo-stochastic matrices and pseudo-positive maps
• Detection of Bidirectional System-Environment Information Exchanges
• Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps
• A solvable class of non-Markovian quantum multipartite dynamics
• Irreversibility mitigation in unital non-Markovian quantum evolutions
• Exchange of information between system and environment: facts and myths
• Optimal evolution models for quantum tomography
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Quantifying non-Markovianity via local quantum Fisher information
• On the Floquet analysis of commutative periodic Lindbladians in finite dimension
• Open system model for quantum dynamical maps with classical noise and corresponding master equations
• Two definitions of the Gell-Mann channels - a comparative analysis
• Memory effects in multipartite systems coupled by non-diagonal dephasing mechanisms
• On the eternal non-Markovianity of non-unital quantum channels
• Robustness and fragility of Markovian dynamics in a qubit dephasing channel
• Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices
• Decoherence of a qubit as a diffusion on the Bloch sphere
• Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information
• Geometry of symmetric and non-invertible Pauli channels
• Dynamics and computation in linear open quantum walks
• Eventually entanglement breaking divisible quantum dynamics
• Quantifying quantum non-Markovianity based on quantum coherence via skew information
• Information back-flow in quantum non-Markovian dynamics and its connection to teleportation
• Pure non-Markovian evolutions
• On the use of total state decompositions for the study of reduced dynamics
• Time-Dependent Dephasing and Quantum Transport
• Non-Markovian processes in quantum theory
• Efficient measure of information backflow with a quasistochastic process
• Entanglement and Optimal Timing in Discriminating Quantum Dynamical Processes
• Efficient and operational quantifier of non-divisibility in terms of channel discrimination