Entangling power of quantum evolutions

We analyze the entangling capabilities of unitary transformations U acting on a bipartite (d(1)xd(2))-dimensional quantum system. To this aim we introduce an entangling power measure e(U) given by the mean linear entropy produced acting with U on a given distribution of pure product states. This measure admits a natural interpretation in terms of quantum operations. For a uniform distribution explicit analytical results are obtained using group-theoretic arguments. The behavior of the features of e(U) as the subsystem dimensions d(1) and d(2) are varied is studied both analytically and numerically. The two-qubit case d(1)=d(2) to be peculiar.