The Channel Matrices for Determining the Entanglement Pattern of Multi-Partite State

We propose the general reduced channel matrices of multi-partite state for determining the entanglement pattern of the state. The matrix elements of reduced channel matrices are nothing but the coefficients of the state so that the rank of channel matrices can be easier determined. The entanglement pattern can be obtained from the evaluation of the rank of reduced matrices in various level of the reduced state. We apply the method on three multi-qubit states as example.