Entanglement of Graph Qutrit States

The number of inequivalent classes of up to 8-qutrit graph states is 1002, with 239 decomposable graphs and 763 indecomposable graphs. Apparently, the former can be decomposed to several indecomposable parts. For qubit graph states, the upper and lower bounds of entanglement have been given. If the two bounds don't coincide, the entanglement can be calculated by iterative method. For qutrit graph states, their lower bounds can be found through the local complementation operations. But its hard to find the upper bound because the qutrit graph states have 2 basis states which are GHZ state and W state. Fortunately, the iterative method can also be used here. In this paper, we calculated the entanglement of all the 1002 graph states. Through researching the results, we found the similar feature with graph qubit states that the decimal part of entanglement is stable.