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We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically uses the Cartan classification of the symmetric spaces of the Lie group SO(n). The resulting factorization of unitary evolutions clearly displays the local and entangling character of each factor.doi:10.1063/1.2245205 fatcat:l35hparrmfbyzm24lv6sak3nke