Abstract:

With the help of the typical generators of special unitary group SU(3) and their properties, a Hamel basis of matrix space M_R(C) was constructed, and its linear independence was proved in detail. Next, using the typical generators of special unitary group SU(R), two Hamel bases of matrix space M_R1R2…_Rn(C) were established, under which a representation of density matrix of a multipartite quantum system was presented, thus providing a theoretical basis for studying  quantum entanglement.

Key words: special unitary group, density matrix, multipartite quantum system, Hamel basis