Determing the entanglement of quantum nonbinary graph states

Abstract

Graph states are multipartite entangled states that correspond to mathematical graphs, where the vertices of the graph now play the role of quantum multilevel systems and edges represent interactions of the systems. Graph states are the basis of quantum error correction and one-way quantum computer. We systematically study the entanglement of non-binary graph states. Using iterative algorithm and entanglement bounds, we calculate the entanglement of all the ternary graph states up to nine vertices and parts of quaternary and quinary graph states modulo local unitary transformations and graph isomorphisms. The entanglement measure can be the geometric measure, the measure of relative entropy of entanglement or the measure of logarithmic robustness. We classify the graph states according to the entanglement values obtained. The closest product states obtained in the calculations are studied.