Abstract
We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics by introducing the coupled harmonic oscillator system. Constructing the ground state ρ₀ and its reduced substate ρ_A = Tr_B ρ₀, we compute two entanglement measures of ρ₀, i.e. E_EoF (ρ₀) = S_von (ρ_A) and E_γ (ρ₀) = S_γ (ρ_A), where S_von and S_γ are the von Neumann and R\'{e}nyi entropies, up to the first order of the GUP parameter α. It is shown that E_γ (ρ₀) increases with increasing α when γ = 2, 3, …. The remarkable fact is that E_EoF (ρ₀) does not have first-order of α. Based on there results we conjecture that E_γ (ρ₀) increases or decreases with increasing α when γ > 1 or γ < 1 respectively for nonnegative real γ.