Related papers: Quantum Entanglement with Generalized Uncertainty Principle

Quantum Entanglement with Generalized Uncertainty Principle

URL: http://arxiv.org/abs/2203.06557v1
Date: Sun, 13 Mar 2022 03:25:46 GMT
Title: Quantum Entanglement with Generalized Uncertainty Principle
Authors: DaeKil Park
Abstract summary: We explore how the quantum entanglement is modified in the generalized uncertainty principle (GUP)-corrected quantum mechanics. It is shown that $cal E_gamma (rho_A)$ increases with increasing $alpha$ when $gamma = 2, 3, cdots$. The remarkable fact is that $cal E_EoF (rho_A)$ does not have first-order of $alpha$.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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 $\rho_A = \mbox{Tr}_B \rho_0$, we compute two entanglement measures of $\rho_0$, i.e. ${\cal E}_{EoF} (\rho_0) = S_{von} (\rho_A)$ and ${\cal E}_{\gamma} (\rho_0) = S_{\gamma} (\rho_A)$, where $S_{von}$ and $S_{\gamma}$ are the von Neumann and R\'{e}nyi entropies, up to the first order of the GUP parameter $\alpha$. It is shown that ${\cal E}_{\gamma} (\rho_0)$ increases with increasing $\alpha$ when $\gamma = 2, 3, \cdots$. The remarkable fact is that ${\cal E}_{EoF} (\rho_0)$ does not have first-order of $\alpha$. Based on there results we conjecture that ${\cal E}_{\gamma} (\rho_0)$ increases or decreases with increasing $\alpha$ when $\gamma > 1$ or $\gamma < 1$ respectively for nonnegative real $\gamma$.

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