On the Entangling Power of Quantum Evolutions

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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 behaviour 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.