Quantum Entanglement with Generalized Uncertainty Principle

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 ${\rho }_0$ and its reduced substate $ρ_A = \mbox{Tr}_B ρ_0$, we compute two entanglement measures of ${\rho }_0$, i.e. ${\mathcal{E}}_{EoF}({\rho }_0)=S_{von}({\rho }_A)$ and ${\mathcal{E}}_{\gamma }({\rho }_0)=S_{\gamma }({\rho }_A)$, where $S_{von}$ and $S_{\gamma }$ are the von Neumann and Rényi entropies, up to the first order of the GUP parameter $\alpha$. It is shown that ${\mathcal{E}}_{\gamma }({\rho }_0)$ increases with increasing $\alpha$ when $\gamma =2,3,\cdots$. The remarkable fact is that ${\mathcal{E}}_{EoF}({\rho }_0)$ does not have first-order of $\alpha$. Based on there results we conjecture that ${\mathcal{E}}_{\gamma }({\rho }_0)$ increases or decreases with increasing $\alpha$ when $\gamma >1$ or $\gamma <1$ respectively for nonnegative real $\gamma$.

17 pages, 4 figures, will appear in Nucl. Phys. B

References in corpus (2)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Computing