论文标题
$ l_ {1}的下限$两部分Qubit-Qudit系统的连贯性及其在检测纠缠的三方Qudit-Qubit-Qudit System中的应用
Lower Bound of $l_{1}$ Norm of Coherence of Bipartite Qubit-Qudit System and its Application in the Detection of Entangled Tripartite Qudit-Qubit-Qudit System
论文作者
论文摘要
量子相干性和量子纠缠是量子信息理论中的两个强大支柱。我们在这里研究量子力学的这两个重要方面之间的任何联系，同时研究纠缠检测问题，以检测两分的较高尺寸纠缠状态和多部分纠缠状态。为了实现我们的目标，我们使用检测到纠缠的标准来得出$ l_ {1} $ $ l_ {1} $相干性的$ l $。此外，我们使用可分离性标准推断出上限$ u $ $ l_ {1} $可分离的两分Qubit-Qudit系统的相干性。因此，我们发现，如果任何$ l_ {1} $两部分Qubit-qudit系统的连贯性范围大于上限$ u $，则给定的Qubit-Qudit状态是纠缠的。 Finally, we obtained the upper bound $U_{1}$ of $l_{1}$ norm of coherence of separable tripartite state lies either in $2 \otimes d \otimes d$ or $d \otimes 2 \otimes d$ or $d \otimes d \otimes 2$ dimensional Hilbert space using the upper bound $U$.我们已经表明，如果任何三方$ qubit-qudit-qudit $或$ qudit-qudit-qudit $或$ qudit-qudit-qudit-qudit-qudit-qubit $ systems的$ l_ {1} $连贯性的范围要大于衍生的上限$ u_ {1} $，则给定的三型三型tripartite System代表一个符合状态。
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable bipartite qubit-qudit system using the separability criterion. Thus, we find that if any $l_{1}$ norm of coherence of bipartite qubit-qudit system is greater than the upper bound $U$ then the given qubit-qudit state is entangled. Finally, we obtained the upper bound $U_{1}$ of $l_{1}$ norm of coherence of separable tripartite state lies either in $2 \otimes d \otimes d$ or $d \otimes 2 \otimes d$ or $d \otimes d \otimes 2$ dimensional Hilbert space using the upper bound $U$. We have shown that if the $l_{1}$ norm of coherence of any tripartite $qubit-qudit-qudit$ or $qudit-qubit-qudit$ or $qudit-qudit-qubit$ system is greater than the derived upper bound $U_{1}$ then the given tripartite system represent an entangled state.
