  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, where 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 does not suggest local maximum
quantum entanglement in our quantum states.
