Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

Abstract

We study the $p$-Rényi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a Rényi version of the entropy power inequality for quantum systems.

Accepted at Int. J. Theor. Phys.(2023)

References in corpus (8)

• Quantum Communication With Zero-Capacity Channels
• Limits on classical communication from quantum entropy power inequalities
• Quantum Entropy and Central Limit Theorem
• The classical capacity of quantum thermal noise channels to within 1.45 bits
• Generic nonadditivity of quantum capacity in simple channels
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Gaussian entanglement witness and refined Werner-Wolf criterion for continuous variables
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems