and, after i log out,all equation cannot be review..ermmm
Qutrits and Tensor Product of )
By
SITI NURUL ‘AIN BINTI ZAITON
December 2009
Chair : Associate Professor Hishamuddin Zainuddin, PhD
Institute : Institute for Matematical Research
The simplest extension from qubit is qutrit. One qutrit can be represented as density matrices using generators of i.e. the eight Gell Mann matrices and the unit 
matrix. Two qutrits give rise to nine-level systems whose complete description involves 81 operators including the identity operator. The aim of this work is to obtain the Lie algebraic structure for two qutrits involving %5Cotimes%20SU(3))
.
By applying tensor product of Gell-Mann matrices, we construct explicit matrix representations of the generators for . These results will be used to compute commutator Lie algebra of . The complete table of the commutator Lie algebra of is constructed by simplifying their expressions in terms of the tensor product basis operators of . We verify not all commutators can be simplified directly to single individual operators, i.e. they involve linear combination of tensor product basis operators of .
In this work, the complete table of commutator algebra of can serve the purpose of identifying Lie subalgebras. The trivial %5Coplus%20su(3))
algebra is easily identifiable but the nontrivial and other subalgebras will require further work. We have also included the case for two qubit studied by Rao et al. in which the trivial and nontrivial subalgebras %5Coplus%20su(2))
are identified. We made small corrections to their results.
