论文标题
量子纠缠与普遍的不确定性原理
Quantum Entanglement with Generalized Uncertainty Principle
论文作者
论文摘要
我们通过引入耦合的谐波振荡器系统来探讨如何在广义不确定性原理（GUP）校正的量子力学中修改量子纠缠。构建基础状态$ρ_0$及其还原的替代$ρ_a= \ mbox {tr}_bρ_0$，我们计算了两个符合$ρ_0$的纠缠度量，即$ {\ cal e} _ {eof} （ρ_0）=s_γ（ρ_a）$，其中$ s_ {von} $和$s_γ$是von neumann和rényi熵，直到Gup参数$α$的一阶。结果表明，$ {\ cal e}_γ（ρ_0）$随着$γ= 2，3，\ cdots $的增加而增加$α$。一个了不起的事实是，$ {\ cal e} _ {eof}（ρ_0）$没有$α$的第一阶。基于那里的结果，我们推测$ {\ cal e}_γ（ρ_0）$增加或减小，当$γ> 1 $> 1 $或$γ<1 $时，非负元$γ$时增加了$α$。
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 $γ$.
