A classical appraisal of quantum definitions of non-Markovian dynamics

Abstract

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behavior is analyzed in detail for quantum dynamics which can be built taking as input a class of classical processes.

15 pages, 6 figures; to appear in J. Phys. B, Special Issue on "Loss of coherence and memory effects in quantum dynamics"

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• Generalized trace distance measure connecting quantum and classical non-Markovianity
• Non-Markovianity of colored noisy channels
• Generalized master equations leading to completely positive dynamics
• Non-Markovianity, coherence and system-environment correlations in a long-range collision model
• Adding dynamical generators in quantum master equations
• Non-Markovian master equations from piecewise dynamics
• Non-Markovian dephasing and depolarizing channels
• Entropy production and correlations in a controlled non-Markovian setting
• Interaction-induced correlations and non-Markovianity of quantum dynamics
• Role of non-Markovianity and backflow of information in the speed of quantum evolution
• Markovian embedding of non-Markovian quantum collisional models
• Experimental investigation of the effect of classical noise on quantum non-Markovian dynamics
• Mixing-induced quantum non-Markovianity and information flow
• The interplay between local and non-local master equations: exact and approximated dynamics
• Generalized trace distance approach to quantum non-Markovianity and detection of initial correlations
• Quantum state tomography with informationally complete POVMs generated in the time domain
• Post-Markovian quantum master equations from classical environment fluctuations
• Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
• On the connection between microscopic description and memory effects in open quantum system dynamics
• Evolution equations for quantum semi-Markov dynamics
• Local disclosure of quantum memory in non-Markovian dynamics
• Asymptotic Floquet states of non-Markovian systems
• Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
• Signatures of non-Markovianity in classical single-time probability distributions
• Equilibrium properties and decoherence of an open harmonic oscillator
• Detecting Non-Markovianity via Linear Entropy of Choi State
• Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system
• Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices
• Entropic witness for quantum memory in open system dynamics
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• On the use of total state decompositions for the study of reduced dynamics
• Hierarchical-environment-assisted non-Markovian and its effect on thermodynamic properties
• Non-Markovian processes in quantum theory