Entanglement Dominance in the Zero-Temperature Limit

We study the low-temperature limit of bosonic continuous-variable systems under Marko
vian thermal environments, with the goal of making precise when entanglement can become
the operationally dominant resource shaping experimentally accessible correlations.
The main technical result is an exact entanglement threshold for symmetric two-mode
squeezed thermal states (TMST), expressed in closed form through the PPT/symplectic
eigenvalue criterion. This provides a controlled benchmark: for fixed squeezing strength,
cooling alone can drive a preparation from separable to entangled below a critical temper
ature.
Building on this benchmark, we propose an entanglement-dominant regime defined
by a timescale inequality between entanglement generation and effective decoherence,
and we outline how this criterion can be mapped to platform-level parameters (damping,
dephasing floors, and thermal occupancies).
Extensions to collective modes and multipartite settings are presented as an outlook
and as a numerical/experimental program, emphasizing what is rigorously proven versus
what is to be tested.