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Journal of Functional Analysis

Interpolations of entanglement breaking channels and equivalent conditions for completely positive maps

Yuan Li, Hong-Ke Du

Published Jan 22, 2015• 23 citations
Publisher
DOI
10.1016/j.jfa.2015.01.008

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Quantum UUU-channels on SSS-spaces
If the symmetry, (an operator JJJ satisfying J=J∗=J−1J=J^*=J^{-1}J=J∗=J−1) which defines the Krein space, is replaced by a (not necessarily self-adjoint) unitary, then we have the notion of an SSS-space which was introduced by Szafraniec. In this paper, we consider SSS-spaces and study the structure of completely UUU-positive maps between the algebras of bounded linear operators. We first give a Stinespring-type representation for a completely UUU-positive map. On the other hand, we introduce Choi UUU-matrix of a linear map and establish the equivalence of the Kraus UUU-decompositions and Choi UUU-matrices. Then we study properties of nilpotent completely UUU-positive maps. We develop the UUU-PPT criterion for separability of quantum UUU-states and discuss the entanglement breaking condition of quantum UUU-channels and explore UUU-PPT squared conjecture. Finally, we give concrete examples of completely UUU-positive maps and examples of 3⊗33 \otimes 33⊗3 quantum UUU-states which are UUU-entangled and UUU-separable.