Two-qutrit Entanglement Witnesses and Gell-Mann Matrices

Details Two-qutrit Entanglement Witnesses and Gell-Mann Matrices Two-qutrit Entanglement Witnesses and Gell-Mann Matrices

2008-02-03

arxiv.org/abs/0802.0270v1

Physics

Quantum Physics

25 pages

Scientific paper

10.1140/epjd/e2008-00041-3

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 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 $\lambda$-diagonal EWs presented in this paper are all decomposable but there exist non-decomposable ones among $\lambda$-non-diagonal EWs.

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