arXiv:2610.13030v1 Announce Type: new Abstract: We study the relationship between strong data-processing inequalities for R\'enyi divergences and hypercontractivity. For R\'enyi divergences of order greater than one, we characterize the contraction of R\'enyi divergences through a property of the dual Markov operator that we name power contraction. Using the contraction coefficient, we derive an upper bound on rectangle probabilities in terms of their marginals that is at least as strong as the corresponding bound obtained via hypercontractivity. Combining this result with inversion of the binary R\'enyi divergence, we derive communication lower bounds for one-way communication-assisted agreement distillation. Examples involving binary symmetric and rare-event Z-channels illustrate the improvements over standard hypercontractive converses.