Operational entanglement of collective quantum modes at room temperature

TL;DR

This paper demonstrates that collective quantum modes can maintain entanglement at room temperature despite thermal noise, providing a minimal framework for certifying macroscopic entanglement through measurable parameters.

Contribution

It derives an exact entanglement boundary for collective modes at finite temperature and links it to measurable noise, bandwidth, dissipation, and coupling parameters.

Findings

Steady-state entanglement can persist at finite temperature in collective modes.

Large collective occupation suppresses but does not eliminate quantum phase diffusion.

Entanglement witnesses are only violated in the quantum regime, confirmed by simulations.

Abstract

Quantum entanglement is commonly assumed to be fragile at ambient temperature and over macroscopic distances, where thermal noise and dissipation are expected to rapidly suppress nonclassical correlations. Here we show that this intuition fails for collective quantum modes whose dynamics is governed by reduced open-system channels rather than by microscopic thermal equilibrium. For two spatially separated collective modes, we derive an exact entanglement boundary based on the positivity of the partial transpose, valid in the symmetric resonant limit. From this result we obtain an explicit minimum collective fluctuation amplitude, expressed entirely in measurable noise, bandwidth, dissipation, and distance-dependent coupling parameters, required to sustain steady-state entanglement at finite temperature. We further show that large collective occupation suppresses but does not eliminate quantum phase diffusion, so the steady state remains phase symmetric and does not collapse to a classical mean-field despite macroscopic signal amplitudes. Stochastic simulations of the reduced open-system dynamics, together with matched classical correlated-noise null models analyzed through an identical pipeline, confirm that entanglement witnesses are violated only in the quantum regime. Our results establish a minimal, platform-independent framework connecting collective-mode dynamics, noise injection, distance, and operational certification of macroscopic entanglement.