Related papers: Requiring linearity leads to complete positivity
We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between…
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
Non-positive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates…
A general method for extending a non-dissipative nonlinear Schr\"odinger and Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles is described. It is shown at a general level that the dynamics so obtained is…
It is known that the existence of memory effect can revive quantum correlations in open system dynamics. In this regard, the backflow of information from environment to the system can be identified with Complete Positive (CP) indivisibility…
We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…
In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of…
It is known that non-unital noise such as the amplitude damping can sometimes increase quantum correlations, while unital noise such as the dephasing usually decreases quantum correlations. It is, therefore, important to delineate the…
In this paper we give a simple sequence of necessary and sufficient finite dimensional conditions for a positive map between certain subspaces of bounded linear operators on separable Hilbert spaces to be completely positive. These…
The simple stationary decoherence of a two-state quantum system is discussed from a new viewpoint of environmental entanglement. My work emphasizes that an unconditional local state must totally be disentangled from the rest of the…
The dynamical equation of hybrid systems, being the combination of Schr\"odinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in…
We investigate in parallel two common pictures used to describe quantum systems interacting with their surrounding environment, i.e., the stochastic Hamiltonian description, where the environment is implicitly included in the fluctuating…
We propose quantization relationships which would let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. The quantum…
Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open system evolution of quantum systems. A canonical structure of the A-map is introduced here. It is shown that this canonical A-map enables…
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…
We study the conditions under which a subsystem code is correctable in the presence of noise that results from continuous dynamics. We consider the case of Markovian dynamics as well as the general case of Hamiltonian dynamics of the system…
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…
A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, but the lack of complete positivity of a quantum evolution (called the "negativity") can be used as a measure of the…