From the aspect of the quantum information theories, various quantum entropies are possibly computed at each stage, which ensures the emergence of the entangled states in the intermediate step. If a single qubit quantum teleportation is near the computational basis, the quantum measurement is dominantly responsible for the joint entropy at the final stage. If it is far from the computational basis, this dominant responsibility is moved into the quantum measurement of system. Therefore, the relative entropy can be regarded as a measure for distance between two different quantum states like trace distance or fidelity. Some relative entropies become infinity, which indicates the non-trivial intersection of the support of one quantum state with kernel of the other quantum state.
