Open-system dynamics of the geometrical reperesentation for a qutrit

The qubit systems have been the central issue of quantum physics and quantum information processing, and various properties and applications concerning about qubits have been extensively discovered and verified experimentally. However, it is nontrivial to generalize the techniques and methods which effectively deal with the problems involving qubits system and is hard to verify their utility for higher dimensional system, for instance a qutrit. In this paper, we employ Gell-Mann basis to parameterize the density operator for three-level systems instead of using Pauli matrices to represent the qubit state. This generalization representation is used to exploit the rich geometric structures and abundant propeties of qutrits. We give the sufficient and necessary conditions for a 3 × 3 Hermitian operator to be positive semidefinite and investigate the dynamical evolution of the geometrical picture for qutrits when exposed to the depolarizing effects induced by the environment.