Maximally entangled states in discrete and Gaussian regimes

We study a relation between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) ones. In the previous work, we have investigated an information-theoretic correspondence between the Gaussian maximally mixed states and their purifications as Gaussian maximally entangled states in Jeong and Lim (Phys Lett A 380:3607, 2016). We here compare the purified continuous-variable maximally entangled state with a two-mode squeezed vacuum state, which is a conventional entangled state in Gaussian regime, by the explicit calculation of quantum fidelities between those states and an N×N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document}-dimensional maximally entangled state in the finite Hilbert space. Consequently, we naturally conclude that the purified maximally entangled state is more suitable to the Gaussian maximally entangled state than the two-mode squeezed vacuum state, in a sense that it might be useful for continuous-variable quantum information tasks in which entangled states are needed.