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We investigate the relationship between strict positivity of the Kossakowski matrix, irreducibility and positivity improvement properties of Markovian Quantum Dynamics. We show that for a Gaussian quantum dynamical semigroup strict…

A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we…

We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system…

The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the…

We consider a recently proposed model of driven open quantum microcircuit [F. Pellegrini et al., Phys. Rev. Lett. 107, 060401 (2011)] amenable to experimental investigations. We show that such an open quantum system provides a concrete…

The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such…

We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Liouvillian reversible dynamics. It connects the ratio between the probabilities of…

Open quantum dynamics in a tripartite scenario including a system, its environment and a passive reference is shown to resolve several open questions regarding not completely positive (NCP) dynamical maps as valid descriptions of open…

The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that every bipartite separable density matrix is temporally…

We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…

Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product…

We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by…

We discuss the case of a Markovian master equation for an open system, as it is frequently found from environmental decoherence. We prove two theorems for the evolution of the quantum state. The first one states that for a generic initial…

The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a…

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the…

We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment…

The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear…

Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. By restricting to dissipative dynamics, here we propose a measure that quantifies how far the environment action on a system…

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…

In order to engineer an open quantum system and its evolution, it is essential to identify and control the memory effects. These are formally attributed to the non-Markovianity of dynamics that manifests itself by the evolution being…