Fixed-Time Gaussian State Transfer via Collective Dissipation in a Fully Static Architecture

Abstract

We establish a fully static, dissipation-only primitive for Gaussian state transfer in which collective coupling to a shared environment fixes a single transfer time without coherent transport or time-dependent control. The dynamics close in a bright--dark decomposition, yielding an analytic transfer time $t^{*} = \pi / g_{a}$ and a real interference factor that eliminates dynamical phase accumulation, so that all phase sensitivity arises solely from the Gaussian fidelity metric. This defines a fixed-time Gaussian communication channel in which dissipation mediates information transfer without active control. Ensemble analysis shows that channel performance remains robust to amplitude-level asymmetries, which act as uniform-rate dressing, whereas phase-level system detuning disrupts the fixed-time mechanism via dynamical phase winding and produces revival behavior. Incorporating finite Ornstein--Uhlenbeck memory via a zeroth-order O-operator expansion yields only rate and phase renormalization without introducing new dynamical pathways. In the fast-memory regime, environmental correlations are rapidly suppressed, rendering the channel insensitive to environmental detuning and restoring the Markovian limit. These results show that collective dissipation alone is sufficient to support fixed-time Gaussian state transfer, challenging the assumption that coherent transport or active control are required for continuous-variable communication.