Quantum non-Markovianity: characterization, quantification and detection.

  title={Quantum non-Markovianity: characterization, quantification and detection.},
  author={{\'A}ngel Rivas and Susana F. Huelga and Martin Bodo Plenio},
  journal={Reports on progress in physics. Physical Society},
  volume={77 9},
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is… 

Figures from this paper

On a concept of quantum non-Markovianity weaker than CP-indivisibility
The problem of defining quantum non-Markovianity has proven elusive, with various inequivalent criteria put forth to address it. We consider the question: what is the weakest notion of quantum
Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems
One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the
When Is a Non-Markovian Quantum Process Classical?
More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here we give an answer to this question for
Non-Markovian Evolution: a Quantum Walk Perspective
This work indicates certain non-Markovian channels that cannot be witnessed by the CP-divisibility criterion, and presents a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measuresuch as mutual information for disambiguation.
Non-Markovian dynamics of open quantum systems
This thesis is centred around the striking phenomenon of non-Markovianity which emanates from exact dynamical descriptions of open quantum systems. NonMarkovianity is associated with the existence of
Quantum non-Markovianity and localization
We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The ``amount'' of non-Markovianity is measured using divisibility and distinguishability
Detecting non-Markovianity via uncertainty relations
We present a formalism for detection of non-Markovianity through uncertainty relations. We show that when there is an information back-flow to the system from its environment through CP-divisibility
Hierarchy of non-Markovianity and k -divisibility phase diagram of quantum processes in open systems
Department of Physics, National Chung Hsing University, Taichung 402, Taiwan(Dated: April 29, 2015)In recent years, much e ort has been devoted to the construction of a proper measure of
A note on the non-Markovianity of quantum semi-Markov processes
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup


Quantum discord and non-Markovianity of quantum dynamics
The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneously-vanishing quantum discord provides a necessary
Markovianity and non-Markovianity in quantum and classical systems
We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition of non-Markovianity of a classical stochastic
Entanglement and non-markovianity of quantum evolutions.
Two different measures of non-markovianity are introduced that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts when complete tomographic knowledge about the evolution is available and when no information whatsoever is available.
Degree of non-Markovianity of quantum evolution.
We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals
Non-Markovian Quantum Probes
We review the most recent developments in the theory of open quantum systems focusing on situations in which the reservoir memory effects, due to long-lasting and non-negligible correlations between
Foundations and measures of quantum non-Markovianity
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
Reveal non-Markovianity of open quantum systems via local operations
Non-Markovianity, as an important feature of general open quantum systems, is usually difficult to quantify with limited knowledge of how the plant that we are interested in interacts with its
Assessing non-Markovian quantum dynamics.
From a snapshot of a quantum evolution, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which a computable measure of "Markovianity" is introduced.
Measure for the non-Markovianity of quantum processes
Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed, which is based on the quantification of the flow of information between the open system and
Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps
We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al.[Phys. Rev. Lett. 103, 210401 (2009);], that is, by