We present a new paradigm for capturing the complementarity of two observables. It is based on the entanglement created by the interaction between the system observed and the two measurement devices used to measure the observables sequentially. Our main result is a lower bound on the entanglement so generated that resembles well-known entropic uncertainty relations. Besides its fundamental interest, this result constitutes a bound on the effectiveness of sequential bipartite operations---corresponding to the measurement interactions---for entanglement generation. We further discuss the intimate connection of our result with two primitives of information processing, namely, decoupling and coherent teleportation. This is joint work with Patrick J. Coles.