Entangling power of quantum evolutions

We analyze the entangling capabilities of unitary transformations U acting on a bipartite ${(d}_{1}\ifmmode\times\else\texttimes\fi{}{d}_{2})$-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 ${d}_{1}{=d}_{2}=2$ is argued to be peculiar.

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