In 2023 Haihambo and Olela Otafudu introduced and studied the notion of quasi-uniform entropy $h_{QU}(\psi)$ for a uniformly continuous self-map $\psi$ of a quasi-metric or a quasi-uniform space $X$. In this talk, we discuss the connection between the topological entropy functions $h, h_f$ and the quasi-uniform entropy function $h_{QU}$ on a quasi-uniform space $X$, where $h$ and $h_f$ are the topological entropy functions defined using compact sets and finite open covers, respectively. In particular, we have shown that for a uniformly continuous self-map $\psi$ of a $T_0$-quasi-uniform space $(X,\mathcal{U})$ we have $h(\psi)\leq h_{QU}(\psi)$ when $X$ is compact and $h_{QU}(\psi)\leq h_f(\psi)$ with equality if $X$ is a compact $T_2$ space.