Set Of Positive Maps Research Articles

Measure of positive and not completely positive single-qubit Pauli maps

The time evolution of an initially uncorrelated system is governed by a completely positive (CP) map. More generally, the system may contain initial (quantum) correlations with an environment, in which case the system evolves according to a not-completely positive (NCP) map. It is an interesting question what the relative measure is for these two types of maps within the set of positive maps. After indicating the scope of the full problem of computing the true volume for generic maps acting on a qubit, we study the case of Pauli channels in an abstract space whose elements represent an equivalence class of maps that are identical up to a non-Pauli unitary. In this space, we show that the volume of NCP maps is twice that of CP maps.

An LMI description for the cone of Lorentz-positive maps II

Let L n be the n-dimensional second-order cone. A linear map from ℝ m to ℝ n is called positive if the image of L m under this map is contained in L n . For any pair (n, m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n − 1)(m − 1) that describes this cone.