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

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. Secondly, we investigate the physical realization of these channels using linear optics, a key platform in photonics. The central research contributions are (i) a new characterization of Gaussian channels in terms of their ampliations, (ii) a precise characterization of the specific pairs of matrices [Formula: see text] that correspond to Gaussian channels physically implementable via linear optical multiport interferometers, (iii) answering the questions posed by Parthasarathy (Parthasarathy KR. 2015 Symplectic dilations, Gaussian states and Gaussian channels. <i>Indian J. Pure Appl. Math.</i> <b>46</b>, 419-439. (doi:10.1007/s13226-015-0144-5)) and (iv) a discussion on some common misunderstandings in the literature. This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.