Quantum Renyi-2 entropy power inequalities for bosonic Gaussian operations

We derive quantum Renyi-2 entropy power inequalities for Gaussian operations of the beam-splitting and squeez-ing type. We first show that known quantum von Neumann entropy power inequalities generalize straightforwardly to quantum Renyi-2 entropy power inequalities for Gaussian states but fail to do so for non-Gaussian states. We then derive quantum Renyi-2 entropy power inequalities that provide lower bounds for the Gaussian operations for any state. The inequality for the squeezing operation is shown to have applications in the generation and detec-tion of quantum entanglement.& COPY; 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement