The information role of entanglement and interference operators in Shor quantum algorithm gate dynamics

Shor algorithm dynamics of quantum computation states are analysed from the classical and the quantum information theory points of view. The Shannon e ntropy is interpreted as the degree of information accessibility through me asurement, while the von Neumann entropy is employed to measure the quantum information of entanglement. The intelligence of a state with respect to a subset of qubits is defined. The intelligence of a state is maximal if the gap between the Shannon and the von Neumann entropy for the chosen result qubits is minimal. We prove that the quantum Fourier transform creates maxi mally intelligent states with respect to the first n qubits for Shor's prob lem, since it annihilates the gap between the classical and quantum entropi es for the first n qubits of every output state.