On quantum additive Gaussian noise channels

TL;DR

This paper characterizes Gaussian quantum channels that can be dilated with passive, number-preserving unitaries, and establishes a normal form showing they are equivalent to applying passive unitaries to an additive Gaussian noise channel.

Contribution

It provides necessary and sufficient conditions for passive dilation of Gaussian channels and introduces a normal form linking such channels to additive Gaussian noise channels.

Findings

Characterization of passively dilatable Gaussian channels

Normal form relating these channels to additive Gaussian noise channels

Conditions involving multi-mode beamsplitters

Abstract

We give necessary and sufficient conditions for a Gaussian quantum channel to have a dilation involving a passive, i.e., number-preserving unitary. We then establish a normal form of such channels: any passively dilatable channel is the result of applying passive unitaries to the input and output of a Gaussian additive channel. The latter combine the state of the system with that of the environment by means of a multi-mode beamsplitter.