Entanglement entropy in the Hamming networks (1503.04986v1)

Abstract: We investigate the Hamming networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and entanglement entropy between two special parts of Hamming network, can be calculated. To this aim, first we use the stratification method to rewrite the adjacency matrix of the network in the stratification basis. Then the entanglement entropy and Schmidt number for special partitions are calculated analytically by using the generalized Schur complement method. Also, we calculate the entanglement entropy between two arbitrary subsets (two equal subsets have the same number of vertices) in H(2; 3) and H(2; 4) numerically, and we give the minimum and maximum values of entanglement entropy in these two Hamming network.