Maximally entangled state and Bell's inequality in qubits

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell's inequality to study intensity of quantum entanglement of maximally entangled states. We use a class of seven-qubit quantum states to demonstrate the method, in which we express all coefficients of the quantum states in terms of concurrences of pure states of a region. When a critical point of an upper bound of Bell's inequality occurs in our quantum states, one of the quantum state is a ground state of the toric code model on a disk manifold. Our result also implies that the maximally entangled states do not suggest local maximum quantum entanglement in our quantum states.