Related papers: Complete positivity on the subsystems level

We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can…

"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative…

We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…

We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We…

Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment…

We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we…

This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather…

One of the most important topics in the study of the dynamics of open quantum system is information exchange between system and environment. Based on the features of a back-flow information from an environment to a system, an approach is…

Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a…

Unital qubit Schwarz maps interpolate between positive and completely positive maps. It is shown that relaxation rates of qubit semigroups of unital maps enjoying Schwarz property satisfy the universal constraint which provides a…

We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times…

Kolmogorov decomposition for a given completely positive definite kernel is a generalization of Paschke's GNS construction for the completely positive map. Using Kolmogorov decomposition, to every quantum dynamical semigroup (QDS) for…

The strong subadditivity condition for the density matrix of a quantum system, which does not contain subsystems, is derived using the qudit-portrait method. An example of the qudit state in the seven-dimensional Hilbert space corresponding…

Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not…