Foundations and Measures of Quantum Non-Markovianity

Abstract

The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.

31 pages, to be published in the special issue: Loss of coherence and memory effects in quantum dynamics, Journal of Physics B: Atomic, Molecular and Optical Physics

References in corpus (12)

• Assessing non-Markovian dynamics
• Non-Markovian quantum jumps
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• On measures of non-Markovianity: divisibility vs. backflow of information
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Initial correlations in open system's dynamics: The Jaynes-Cummings model
• Exciton-phonon information flow in the energy transfer process of photosynthetic complexes
• Lindblad rate equations
• Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• On the Contractivity of Hilbert-Schmidt distance under open system dynamics

Cited by in corpus (24)

• Quantum trajectories and open many-body quantum systems
• Collision-model-based approach to non-Markovian quantum dynamics
• Quantum regression theorem and non-Markovianity of quantum dynamics
• Non-Markovianity through flow of information between a system and an environment
• Harnessing non-Markovian quantum memory by environmental coupling
• Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
• Quantum-speed-limit time for multiqubit open systems
• Quantum Speed Limit Bounds in an Open Quantum Evolution
• Heat flux dynamics in dissipative cascaded systems
• Precursors of non-Markovianity
• Non-Markovianity and memory effects in quantum open systems
• General structure of quantum collisional models
• Quantum non-Markovian piecewise dynamics from collision models
• Correction to the geometric phase by structured environments: the onset of non-Markovian effects
• Quantum non-Markovianity induced by Anderson localization
• Optimal Control of Quantum Measurement
• Relaxation of quantum dots in a magnetic field at finite bias -- charge, spin and heat currents
• Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems
• Waveguide-QED-based measurement of a reservoir spectral density
• Microscopic modelling of general time-dependent quantum Markov processes
• Different types of open quantum systems evolving in a Markovian regime
• Decoherence of an entangled state of a strongly-correlated double quantum dot structure through tunneling processes
• Emergence of non-Markovianity in the emission process of an atom in a half-cavity
• Frontiers of open quantum system dynamics