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arXiv 2203.06557quant-phhep-th
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广义不确定原理下的量子纠缠

Quantum Entanglement with Generalized Uncertainty Principle

DaeKil Park

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

在广义不确定原理（GUP）修正的量子力学中，通过引入耦合谐振子系统，研究了量子纠缠是如何被修正的。构造了基态$ρ_0$及其约化子态$ρ_A = \mbox{Tr}_B ρ_0$，计算了$ρ_0$的两种纠缠度量：${\cal E}_{EoF} (ρ_0) = S_{von} (ρ_A)$和${\cal E}_γ (ρ_0) = S_γ (ρ_A)$，其中$S_{von}$和$S_γ$分别是到GUP参数$α$的一阶的von Neumann和Rényi熵.结果表明，当${\cal E}_γ (ρ_0)$。值得注意的事实是，${\cal E}_{EoF} (ρ_0)$没有一阶$α$。根据这些结果，我们推测当$γ> 1$或$γ< 1$分别为非负实数$γ$时，${\cal E}_γ (ρ_0)$随$α$的增加而增加或减少.

英文摘要：

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

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