Exceptional points in Gaussian channels: diffusion gauging and drift-governed spectrum

TL;DR

This paper establishes a principle that the spectral properties of Gaussian channels are governed solely by drift when diffusion is gauged away, providing explicit transformations and illustrating with examples including non-Markovian channels.

Contribution

It extends the noise-independence principle to Gaussian channels, introducing explicit Gaussian similarity transformations to gauge away diffusion in both continuous and discrete time.

Findings

Eigenvalues depend only on drift for Hurwitz cases.

Explicit Gaussian similarity transformations are constructed.

Exceptional-point manifolds are analytically obtained for examples.

Abstract

McDonald and Clerk [Phys.\ Rev.\ Research 5, 033107 (2023)] showed that for linear open quantum systems the Liouvillian spectrum is independent of the noise strength. We first make this noise-independence principle precise in continuous time for multimode bosonic Gaussian Markov semigroups: for Hurwitz drift, a time-independent Gaussian similarity fixed by the Lyapunov equation gauges away diffusion for all times, so eigenvalues and non-diagonalizability are controlled entirely by the drift, while diffusion determines steady states and the structure of eigenoperators. We then extend the same separation to discrete time for general stable multimode bosonic Gaussian channels: for any stable Gaussian channel, we construct an explicit Gaussian similarity transformation that gauges away diffusion at the level of the channel parametrization. We illustrate the method with a single-mode squeezed-reservoir Lindbladian and with a non-Markovian family of single-mode Gaussian channels, where the exceptional-point manifolds and the associated gauging covariances can be obtained analytically.