Figure 3: (Color online) The average absolute value of the change Δ G ( ψ ) in the entanglement, defined in Eq. (33), induced by the QFT for a sample of random quantum states (a) and for periodic states (b), as a function of the number of qubits, q . The random states are taken from a uniform distribution on the 2 q -dimensional complex unit sphere. For the periodic states, the average is over all periodic states with a given number of qubits. For the random states the error bars represent one standard deviation in each direction, while for the periodic states the distribution is extremely narrow, much narrower than the width of the line. 22 3 4 5 6 7 8 9 10 11 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 q | Δ G ( ψ ) | (a) 3 4 5 6 7 8 9 10 11 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 q | Δ G ( ψ ) | (b)