An effective method of investigation of positive maps on the set of positive definite operators |
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Authors: | A Jamio?kowski |
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Institution: | Institute of Theoretical Physics, Nicholas Copernicus University, Toruń, Poland |
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Abstract: | Let 1 be the algebra of linear operators on the n-dimensional Hilbert space 1, and let 2 be the algebra of linear operators of the m-dimensional Hilbert space 2. Let (1, 2) denote the complex space of linear maps from 1 to 2. By a positive map we mean an element of the space (1, 2) (superoperator with respect to 1) which maps positive definite operators in 1 into positive definite operators in 2. The aim of this paper is to present an effective method which allows to verify whether a given superoperator Λ∈(1, 2) is a positive map. Besides that necessary and sufficient conditions for the positive definiteness of even-degree forms in many variables are given. |
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