Related papers: Unital Positive Maps and Quantum States

The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.

The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…

Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and…

Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive…

We introduce a framework for the construction of completely positive maps for subsystems of indistinguishable fermionic particles. In this scenario, the initial global state is always correlated, and it is not possible to tell system and…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…

Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…

In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…

Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…

We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived…

We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…

For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…

We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…

We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…

Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We…

We study k-positive maps on operators. Proofs are given to different positivity criteria. Special attention is on positive maps arising in the study of quantum information science. Results of other researchers are extended and improved. New…