The statistics of the entanglement generated by the Hadamard-CNOT quantum circuit

We consider the change of entanglement of formation ΔE produced by the Hadamard-CNOT circuit on a general (pure or mixed) state ρ describing a system of two qubits. We study numerically the probabilities of obtaining different values of ΔE, assuming that the initial state is randomly distributed in the space of all states according to the product measure introduced by Zyczkowski et al. (Phys. Rev. A 58 (1998) 883).