Positive Maps Which Are Not Completely Positive

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.

4pages,The Institute of Theoretical Physics, Academia Sinica, Beijing 100080, P.R. China

References in corpus (1)

• Canonical Quantum Teleportation

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