Some statistical features of the entanglement changes associated with quantum logical gates

We investigate the changes in the entanglement of formation ΔE produced by quantum logical gates acting on composite quantum systems. We consider two-qubit, three-qubit, and two-qutrit systems. We prove that the ΔE-distributions generated by different quantum gates that can be obtained from each other by recourse to appropriate local unitary transformations are identical, even if these gates (in general) produce different changes of entanglement on individual states. We also study, numerically, some features of the probabilities for obtaining different values of ΔE. In the case of two-qubit we show that the ΔE-distributions are well fitted by simple q-MaxEnt distributions.