Two-qutrit entanglement witnesses and Gell-Mann matrices

The Gell-Mann lambda 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 rising 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 A-diagonal EWs presented in this paper are all decomposable but by adding A-non-diagonal terms, one can obtain various non-decomposable EWs.