A Comparison of Bipartite N-Qubit States to Classify Entangled States under Symmetric Consideration

We show the relation between partition and the permutation symmetry for bipartite N-qubits via Young tableaux. The word and weight formalism of Young tableaux provide a simple way of quantum comparison and we use this comparison together with partition to classify bipartite N-qubit states as different entanglement classes each of which has an entanglement index.