The relation of entanglement to the number of qubits and interactions between them for different graph states

Abstract

We quantify the entanglement and its variations via generalized concurrence, Meyer–Wallach measure and its generalizations. Then we investigate the interactions between qubits on complete graphs, tree graphs, chain graphs and loop graphs with 3 to 8 qubits. It is observed that the amount of all entanglement measures in tree graph in the first group of considered graphs, are equal. The complete equivalent graph is equal and the entanglement measures for these graphs change altering the number of qubits. Furthermore, it can be seen that the entanglement measures are increased augmenting the number of qubits in the chain graph and loop graph. The entanglement of loop graphs is equal to or greater than the entanglement of chain graphs assuming the same number of qubits. Also there is a significant relation between entanglement, number of qubits, and interactions between qubits for the second group of considered graphs. As the number of interactions (presented by edges) increases between the qubits, the entanglements increase in these states. It is shown that the employed entanglement measures reveal the different values changing the number of qubits (vertices).