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We derive a family of entanglement criteria for continuous variable systemsbased on the R\'enyi entropy of complementary distributions. We show that theseentanglement witnesses can be more sensitive than those based on second-ordermoments, as well as previous tests involving the Shannon entropy [Phys. Rev.Lett. \textbf{103}, 160505 (2009)]. We extend our results to include the caseof discrete sampling, and develop another set of entanglement tests using thediscrete Tsallis entropy. We provide several numerical results which show thatour criteria can be used to identify entanglement in a number of experimentallyrelevant quantum states.

A Family of Continuous Variable Entanglement Criteria using General Entropy Functions