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Positive Maps Which Are Not Completely Positive

Sixia Yu
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Abstract

The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix representation of Hermitian linear map, we show that every positive map which is not completely positive is a {\em difference} of two completely positive maps. A necessary and sufficient condition for a positive map which is not completely positive is also presented, which is illustrated by some examples.

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Sixia Yu. 2000-01-14. Positive Maps Which Are Not Completely Positive. https://doi.org/10.1103/physreva.62.024302

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