Quantum Entanglement with Generalized Uncertainty Principle
| Autor: | Park, DaeKil |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2022.115736 |
| Popis: | 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 $\gamma$. Comment: 17 pages, 4 figures, will appear in Nucl. Phys. B |
| Databáze: | arXiv |
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