  Separability conditions for a bipartite quantum system of finite-dimensional
subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic
uncertainty relations often lead to entanglement criteria. We propose new
approach based on the convolution of discrete probability distributions.
Measurements on a total system are constructed of local ones according to the
convolution scheme. Separability conditions are derived on the base of
uncertainty relations of the Maassen-Uffink type as well as majorization
relations. On each of subsystems, we use a pair of sets of subnormalized
vectors that form rank-one POVMs. We also obtain entropic separability
conditions for local measurements with a special structure, such as mutually
unbiased bases and symmetric informationally complete measurements. The
relevance of the derived separability conditions is demonstrated with several
examples.
