  We find that the purifications of several Gaussian maximally mixed states
(GMMSs) correspond to some Gaussian maximally entangled states (GMESs) in the
continuous-variable regime. Here, we consider a two-mode squeezed vacuum (TMSV)
state as a purification of the thermal state and construct a general formalism
of the Gaussian purification process. Moreover, we introduce other kind of
GMESs via the process. All of our purified states of the GMMSs exhibit Gaussian
profiles; thus, the states show maximal quantum entanglement in the Gaussian
regime.
