Related papers: Positive Maps Which Are Not Completely Positive
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…
Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…
We introduce a nonsymmetric real matrix which contains all the information that the usual Hermitian density matrix does, and which has exactly the same tensor product structure. The properties of this matrix are analyzed in detail in the…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.
The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment…
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…
Two long standing open problems in quantum theory are to characterize the class of initial system-bath states for which quantum dynamics is equivalent to (1) a map between the initial and final system states, and (2) a completely positive…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
We introduce a property of a matrix-valued linear map $\Phi$ that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be if every quantum state supported on the subspace is…
Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…
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…
Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It is shown that this class gives rise to a new characterization of entangled states. Additionally, it provides a refinement of the…
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…
For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…