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We study the $p$-R\'{e}nyi entropy power inequality with a weight factor $t$on two independent continuous random variables $X$ and $Y$. The extensionessentially relies on a modulation on the sharp Young's inequality due toBobkov and Marsiglietti. Our research provides a key result that can be used asa fundamental research finding in quantum Shannon theory, as it offers aR\'{e}nyi version of the entropy power inequality for quantum systems.

Weighted $p$-R\'{e}nyi Entropy Power Inequality: Information Theory to Quantum Shannon Theory