Purification of Gaussian maximally mixed states

•Candidates of Gaussian maximally mixed state are proposed.•Obtaining Gaussian maximally entangled states using the purification process.•The suggested states can be applicable for the test of capacity problem in Gaussian regime.

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.