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Abstract
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The Gell-Mann λ matrices for Lie algebra su(3) are the natural basis for the Hilbert space of
Hermitian operators acting on the states of a three-level system(qutrit). So the construction of EWs for
two-qutrit states by using these matrices may be an interesting problem. In this paper, several two-qutrit
EWs are constructed based on the Gell-Mann matrices by using the linear programming (LP) method
exactly or approximately. The decomposability and non-decomposability of constructed EWs are also
discussed and it is shown that the λ-diagonal EWs presented in this paper are all decomposable but by
adding λ-non-diagonal terms, one can obtain various non-decomposable EWs.
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