Entangling power of quantum evolutions

We analyze the entangling capabilities of unitary transformations U acting on a bipartite ${(d}_1\times d_2)$-dimensional quantum system. To this aim we introduce an entangling power measure $e\left(U\right)\mathrm{}$ 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 $e\left(U\right)\mathrm{}$ as the subsystem dimensions $d_1$ and $d_2$ are varied is studied both analytically and numerically. The two-qubit case $d_1{=d}_2=2\mathrm{}$ is argued to be peculiar.