Hierarchy of Non-Markovianity and $k$-divisibility phase diagram of Quantum Processes in Open Systems

Abstract

In recent years, much effort has been devoted to the construction of a proper measure of quantum non-Markovianity. However, those proposed measures are shown to be at variance with different situations. In this work, we utilize the theory of $k$-positive maps to generalize a hierarchy of $k$-divisibility and develop a powerful tool, called $k$-divisibility phase diagram, which can provide a further insight into the nature of quantum non-Markovianity. By exploring the phase diagram with several paradigms, we can explain the origin of the discrepancy between two frequently used measures and find the condition under which the two measures coincide with each other.

5 pages, 4 figures

References in corpus (11)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Assessing non-Markovian dynamics
• On the degree of non-Markovianity of quantum evolution
• On measures of non-Markovianity: divisibility vs. backflow of information
• Observation of Dicke Superradiance for Two Artificial Atoms in a Cavity with High Decay Rate
• Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems
• Finding the Kraus decomposition from a master equation and vice versa
• Comparative study of non-Markovianity measures in exactly solvable one and two qubit models
• Non-Markovian random unitary qubit dynamics
• Competition between memory-keeping and memory-erasing decoherence channels
• The Jamiołkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number $k$ and $k$-positive maps

Cited by in corpus (16)

• Controlling open quantum systems: Tools, achievements, and limitations
• Eternal non-Markovianity: from random unitary to Markov chain realisations
• Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics
• Vibration-induced coherence enhancement of the performance of a biological quantum heat engine
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• Entanglement negativity as a universal non-Markovianity witness
• Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
• Non-Markovianity, information backflow and system-environment correlation for open-quantum-system processes
• Quantifying Quantum-Mechanical Processes
• Quantifying non-Markovianity via conditional mutual information
• Generalized formalism for information backflow in assessing Markovianity and its equivalence to divisibility
• Exchange of information between system and environment: facts and myths
• Non-Markovianity of photon dynamics in a birefringent crystal
• Effects of symmetry breaking of the structurally-disordered Hamiltonian ensembles on the anisotropic decoherence of qubits
• Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information
• Photonic non-Markovianity identification by quantum process capabilities of non-CP processes