Criterion for Genuine Multipartite Entanglement Quantum Channels

We introduce a character matrix for the N-qubit subsystem of a 2N-qubit state and show the criterion for genuine entanglement channel existing between two N-qubit subsystems in the state. The criterion allows us to check conveniently whether genuine quantum channels exist or not in the 2N-qubit state without calculating its N-qubit reduced density matrices.