Entangling power of quantum evolutions

We analyze the entangling capabilities of unitary transformations U acting on a bipartite (d₁×d₂)-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 d₁ and d₂ are varied is studied both analytically and numerically. The two-qubit case d₁=d₂=2 is argued to be peculiar.