On positive linear maps between matrix algebras
نویسندگان
چکیده
منابع مشابه
A Problem Relating to Positive Linear Maps on Matrix Algebras
As usually, a density matrix of M, is understood to be a non-negative matrix with trace equal to one. Thus, stochastic mappings are exactly those linear maps on M, which carry density matrices into density matrices. In this paper we shall deal with a particular case of the following problem concerning density matrices and stochastic transformations: Give necessary and sufficient conditions unde...
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We will be concerned with linear positive maps φ : Mm(C) → Mn(C). To fix notation we begin with setting up the notation and the relevant terminology (cf. [7]). We say that φ is positive if φ(A) is a positive element in Mn(C) for every positive matrix from Mm(C). If k ∈ N, then φ is said to be k-positive (respectively k-copositive) whenever [φ(Aij)] k i,j=1 (respectively [φ(Aji)] k i,j=1) is pos...
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Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1986
ISSN: 0024-3795
DOI: 10.1016/0024-3795(86)90290-9