What is a Gaussian channel, and when is it physically implementable using a multiport interferometer?

TL;DR

This paper unifies the theoretical definitions of quantum Gaussian channels and characterizes when they can be physically realized using multiport interferometers, linking abstract models to practical optical implementations.

Contribution

It provides a rigorous proof of the equivalence of key definitions of quantum Gaussian channels and characterizes the parameters for their physical implementation via multiport interferometers.

Findings

Unified framework for quantum Gaussian channels

Characterization of implementable channels using multiport interferometers

Resolved open questions on physical realizability

Abstract

Quantum Gaussian channels are fundamental models for communication and information processing in continuous-variable quantum systems. This work addresses both foundational aspects and physical implementation pathways for these channels. Firstly, we provide a rigorous, unified framework by formally proving the equivalence of three principal definitions of quantum Gaussian channels prevalent in the literature, consolidating theoretical understanding. Secondly, we investigate the physical realization of these channels using multiport interferometers, a key platform in quantum optics. The central research contribution is a precise characterization of the channel parameters that correspond to Gaussian channels physically implementable via linear optical multiport interferometers. This characterization bridges the abstract mathematical description with concrete physical architectures. Along the way, we also resolve some questions posed by Parthasarathy (Indian J. Pure Appl. Math. 46, (2015)).