Quantum Rényi-2 entropy power inequalities for bosonic Gaussian operations

Abstract

We derive quantum Rényi-2 entropy power inequalities for Gaussian operations of the beam-splitting and squeezing type. We first show that known quantum von Neumann entropy power inequalities generalize straightforwardly to quantum Rényi-2 entropy power inequalities for Gaussian states but fail to do so for non-Gaussian states. We then derive quantum Rényi-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 detection of quantum entanglement.