Probing the structure of Gaussian covariant operations

In this work, we dive into one of the most fundamental constraints in physics, i.e. time-translation symmetry, and ask how it shapes the dynamics of continuous-variable, Gaussian quantum systems (think quantum optics, modes of light, harmonic oscillators). Gaussianity is well understood. Time-translation covariance is well understood. But when both constraints are imposed simultaneously…..

Over the past year or two, a team of friends set out on unentangling this problem together. The result is a rigorous classification of Gaussian quantum operations that respect time-translation symmetry. Upon scrutiny, we find interestingly that several intuitions and structural results that hold in the discrete-variable setting…. don’t quite translate over! Most interestingly, we find monotones that are a little unorthodox, which leads to e.g. the vanishing of catalytic advantage.

Another surprise appears when we add thermodynamic structure. When we further impose Gibbs preservation, the familiar gap between thermal operations and Gibbs-preserving covariant channels disappears in the Gaussian setting. While the existence of this gap is well known, the physical mechanisms behind it have been less clear. Our results identify the first concrete ingredient that closes it. We suspect, though, there is still more to uncover.

Real-world quantum systems are often subject to multiple constraints at once. What this project taught us is that their interplay can produce structures far richer than what one would guess from studying each ingredient in isolation. Stay tuned to another quest we recently completed on this topic ;) meanwhile, find out about our ``Gibbs-preserving, Gaussian Phase-Covariant (GPGPC)” exploration in this preprint!