Quantum Rényi entropy functionals for bosonic Gaussian systems

Abstract

In this study, the quantum Rényi entropy power inequality of order p>1 and power κ 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.