Quantum R\'{e}nyi Entropy Functionals for Bosonic Gaussian Systems
- URL: http://arxiv.org/abs/2204.10737v3
- Date: Tue, 24 Oct 2023 08:02:30 GMT
- Title: Quantum R\'{e}nyi Entropy Functionals for Bosonic Gaussian Systems
- Authors: Junseo Lee and Kabgyun Jeong
- Abstract summary: We introduce a quantum analog of the classical R'enyi-$p$ entropy power inequality.
The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities.
- Score: 1.0619039878979954
- License: http://creativecommons.org/licenses/by/4.0/
- 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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