Entropy power inequalities and classical capacities of bosonic noise channels

Characterizing information-carrying capacities of bosonic communication channels is of significant practical interest. For thermal noise channels, using coherent (product) states yields an achievable rate for classical communication which is conjectured to be optimal. However, it is not known whether coding strategies using entanglement may perform better. Here we discuss upper bounds on classical capacities of thermal noise channels. These imply that coherent-state coding is close to optimal. Our main tool is a quantum analog of the entropy power inequality introduced Shannon. It gives a lower bound on the output von Neumann entropy when two independent signals combine at a beamsplitter.