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One of the most important and useful entropic uncertainty relations concernsa $d$ dimensional system and two mutually unbiased measurements. In such asetting, the sum of two information entropies is lower bounded by $\ln d$. Ithas recently been shown that projective measurements subject to operationalmutual unbiasedness can also be constructed in a continuous domain, with thehelp of periodic coarse graining. Here we consider the whole family of R\'enyientropies applied to these discretized observables and prove that such a schemedoes also admit the uncertainty relation mentioned above.

Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts