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arXiv · 2204.10737

Quantum R\'{e}nyi Entropy Functionals for Bosonic Gaussian Systems

Junseo Lee·Kabgyun Jeong
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Abstract

In this study, the quantum R\'{e}nyi entropy power inequality of order $p>1$ and power $\kappa$ is introduced as a quantum analog of the classical R\'{e}nyi-$p$ 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 R\'{e}nyi-$p$ 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.

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Junseo Lee, Kabgyun Jeong. 2022-04-22. Quantum R\'{e}nyi Entropy Functionals for Bosonic Gaussian Systems. https://doi.org/10.1016/j.physleta.2023.129183

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