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Entanglement criteria for an $n$-partite quantum system with continuousvariables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropiesare widely used as a good information measure due to many nice properties.Derived entanglement criteria are based on several mathematical results such asthe Hausdorff-Young inequality, Young's inequality for convolution and itsconverse. From the historical viewpoint, the formulations of these results withsharp constants were obtained comparatively recently. Using the position andmomentum observables of subsystems, one can build two total-system measurementswith the following property. For product states, the final density in eachglobal measurement appears as a convolution of $n$ local densities. Hence,restrictions in terms of two R\'{e}nyi entropies with constrained entropicindices are formulated for $n$-separable states of an $n$-partite quantumsystem with continuous variables. Experimental results are typically sampledinto bins between prescribed discrete points. For these aims, we giveappropriate reformulations of the derived entanglement criteria.

R\'enyi formulation of entanglement criteria for continuous variables