Related papers: When the assignment map is completely positive
We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two…
Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [W. A. Majewski, L.E. Labuschagne, Ann. H. Poincare. 15, 1197-1221, (2014)] where we made a strong case for…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…
We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely…
For an open quantum system to evolve under CPTP maps, assumptions are made on the initial correlations between the system and the environment. Hermitian-preserving trace-preserving (HPTP) maps are considered as the local dynamic maps beyond…
Coecke and Heunen described completely positive maps in dagger monoidal categories and the {\sf CP}-infinity construction on these categories in order to construct a category of arbitrary dimensional quantum processes. This article…
Many quantum control problems are formulated as a search for an optimal field that maximizes a physical objective. This search is performed over a landscape defined as the objective as a function of the control field. A recent Letter [A. N.…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
Power law systems have been studied extensively due to their wide-ranging applications, particularly in chemistry. In this work, we focus on power law systems that can be decomposed into stoichiometrically independent subsystems. We show…
An operator convex function on (0,\infty) which satisfies the symmetry condition k(1/x) = x k(x) can be used to define a type of non-commutative multiplication by a positive definite matrix (or its inverse) using the primitive concepts of…
We consider a class of quantum dissipative systems governed by a one parameter completely positive maps on a von-Neumann algebra. We introduce a notion of recurrent and metastable projections for the dynamics and prove that the unit…
We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We…
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…
Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the…
This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…