Quantum entanglement with generalized uncertainty principle

We explore how the quantum entanglement is modified in generalized uncertainty principle (GUP)-corrected mechanics by introducing coupled harmonic oscillator system. Constructing ground state $\rho_0$ and its reduced substate $\rho_A = \mbox{Tr}_B \rho_0$, we compute two measures of $\rho_0$, i.e. ${\cal E}_{EoF} (\rho_0) S_{von} (\rho_A)$ E}_{\gamma} S_{\gamma} (\rho_A)$, where $S_{von}$ $S_{\gamma}$ are von Neumann R\'{e}nyi entropies, up to first order GUP parameter $\alpha$. It shown that (\rho_0)$ increases with increasing $\alpha$ when $\gamma 2, 3, \cdots$. The remarkable fact does not have first-order Based on there results conjecture or decreases > 1$ < respectively for nonnegative real $\gamma$.