A completely positive map associated with a positive map

2010/09/29 by Størmer, Erling · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1009.5809

Abstract

We show that each positive map from B(K) to B(H) with K and H finite dimensional Hilbert spaces is a scalar multiple of a map of the form Tr - ψ with ψ completely positive. This is used to give necessary and sufficient conditions for maps to be C-positive for a large class of mapping cones; in particular we apply the results to k-positive maps.

Cited by

• k-Positive Maps: New Characterizations and a Generation Method

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