Related papers: Requiring linearity leads to complete positivity

In this paper, we investigate the entanglement dynamics of a two qutrits system interacting with a spin environment. Using negativity as the entanglement measure, we study the entanglement dynamics of the system. The calculations show that…

We prove that the environment induced entanglement between two non interacting, two-dimensional quantum systems S and P can be used to control the dynamics of S by means of the initial state of P. Using a simple, exactly solvable model, we…

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial…

We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…

The common wisdom in the field of quantum information theory is that when a system is initially correlated with its environment, the map describing its evolution may fail to be completely positive. If true, this would have practical and…

This thesis presents studies performed on open quantum systems, that is, quantum systems interacting with their surrounding environment. Such systems are important not only in understanding the quantum-to-classical transition but also for…

In coherent quantum feedback control schemes, a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled 'indirectly' through the interaction with…

Many processes in nature seem to be entirely controlled by transition rates and the corresponding statistical dynamics. Some of them are in essence quantum, like the decay of excited states, the tunneling through barriers or the decay of…

We argue that usual quantum statics and the dynamical equivalence of mixed quantum states to {\it probabilistic mixtures}suffice to guarantee a linear evolution law, which necessarily complies with the no-signaling condition. Alternatively,…

The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…

Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…

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…

A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…

We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.

We investigate the equilibration and thermalization properties of quantum systems interacting with a finite dimensional environment. By exploiting the concept of time averaged states, we introduce a completely positive map which allows to…

The paper shows that positive linear systems can be stabilized using positive Luenberger-type observers. This is achieved by structuring the observer as monotonically converging upper and lower bounds on the state. Analysis of the…

The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be…

We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical…

The majority of quantum open system models in the literature are simplistic in the sense that they only explicitly account for that part of the environment that directly interacts with the system of interest. A quantum open system with an…

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…