Eur. Phys. J. D 47, 283-293 (2008)
https://doi.org/10.1140/epjd/e2008-00041-3

Two-qutrit entanglement witnesses and Gell-Mann matrices

¹ Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz, 51664, Iran
² Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-1795, Iran
³ Research Institute for Fundamental Sciences, Tabriz, 51664, Iran

Corresponding authors: ^a jafarizadeh@tabrizu.ac.ir - ^b y-akbari@tabrizu.ac.ir - ^c behzadi@tabrizu.ac.ir

Received: 18 September 2007
Revised: 3 February 2008
Published online: 14 March 2008

Abstract

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.