Minimum output entropy of Gaussian channels

Abstract

We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.

This paper has been withdrawn by the authors due to incompleteness of proof. The argument is accurate up to in the second minimization (equations (4-5)). At this point, a subtlety of minimization theory arises: the gradients of the constraints in the Lagrange minimization are not linearly independent. Accordingly, although we do indeed find that thermal states minimize the output entropy, the Lagrange theorem no longer guarantees the uniqueness of the solution