The optimal unitary dilation for bosonic Gaussian channels

TL;DR

This paper determines the minimal environmental modes needed for unitary dilation of bosonic Gaussian channels, providing explicit constructions and simplifying their characterization for quantum information transmission.

Contribution

It computes the minimal number of modes for pure environments and presents explicit dilations, advancing the understanding of continuous-variable quantum channels.

Findings

Explicit unitary dilation for arbitrary bosonic Gaussian channels

Minimal environmental modes for pure and mixed environments identified

Simplifies the analysis of continuous-variable quantum channels

Abstract

A generic quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. Here, the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multi-mode bosonic Gaussian channel is analyzed both for mixed and pure environment corresponding to the Stinespring representation. In particular, for the case of pure environment we compute this quantity and present an explicit unitary dilation for arbitrary bosonic Gaussian channel. These results considerably simplify the characterization of these continuous-variable maps and can be applied to address some open issues concerning the transmission of information encoded in bosonic systems.