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We study a general corresponding principle between discrete-variable quantumstates and continuous-variable (especially, restricted on Gaussian) states viaquantum purification method. In the previous work, we have already investigatedan information-theoretic correspondence between the Gaussian maximally mixedstates (GMMSs) and their purifications known as Gaussian maximally entangledstates (GMESs) in [Phys. Lett. A {\bf 380}, 3607 (2016)]. We here compare an$N\times N$-dimensional maximally entangled state to the GMES we proposedpreviously, through an explicit calculation of quantum fidelity between thoseentangled states. By exploiting the results, we naturally conclude that ourGMES is more suitable to the concept of \emph{maximally entangled} state inGaussian quantum information, and thus it might be useful or applicable forquantum information tasks than the two-mode squeezed vacuum (TMSV) state in theGaussian regime.

Correspondence between maximally entangled states in discrete and Gaussian regimes