  A quantum channel will have a Choi representation from which the complete
positivity (CP) can be determined in a number of different ways. Every method
relies on Choi's proof which relates CP to the positive semi-definiteness of a
specially constructed matrix (i.e. the "Choi representation of the channel").
It can be shown that different CP tests can be used in different situations to
avoid the computationally expensive brute force method of calculating the full
spectrum of the Choi representation, which is the traditional method for
testing whether or not a channel is CP. It is important to have quick, reliable
analytical and computational tests for CP as negative channels become more
prevalent in the study of quantum information.
