Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems

Abstract

In this study, the quantum Rényi entropy power inequality of order $p>1$ and power $\kappa$ is introduced as a quantum analog of the classical Rényi-$p$ entropy power inequality. To derive this inequality, we first exploit the Wehrl-$p$ entropy power inequality on bosonic Gaussian systems via the mixing operation of quantum convolution, which is a generalized beam-splitter operation. This observation directly provides a quantum Rényi-$p$ entropy power inequality over a quasi-probability distribution for $D$-mode bosonic Gaussian regimes. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities, particularly universal upper bounds on bosonic Gaussian quantum channels, and a Gaussian entanglement witness in the case of Gaussian amplifier via squeezing operations.

arXiv comment7 pages, 1 figure, 1 table; Close to published version

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Cited by in corpus (2)

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory