Parametrized multipartite entanglement measures

作者：Hui Li, Ting Gao, Fengli Yan · 发表于：Physical Review A · 年份：2024 · DOI：10.1103/physreva.109.012213 · 被引用次数：21 · 研究领域：Quantum Information and Cryptography、Quantum Mechanics and Applications、Quantum Computing Algorithms and Architecture

We investigate parametrized multipartite entanglement measures from the perspective of $k$ nonseparability in this paper. We present two types of entanglement measures in $n$-partite systems, $q\text{\ensuremath{-}}k\text{\ensuremath{-}}\mathrm{ME}$ concurrence $(q>1,\phantom{\rule{0.28em}{0ex}}2\ensuremath{\le}k\ensuremath{\le}n)$ and $\ensuremath{\alpha}\text{\ensuremath{-}}k\text{\ensuremath{-}}\mathrm{ME}$ concurrence $(0\ensuremath{\le}\ensuremath{\alpha}<1,\phantom{\rule{0.28em}{0ex}}2\ensuremath{\le}k\ensuremath{\le}n)$, which unambiguously detect all $k$-nonseparable states in arbitrary $n$-partite systems. Rigorous proofs show that the proposed $k$-nonseparable measures satisfy all the requirements for being an entanglement measure including the entanglement monotone, strong monotone, convexity, vanishing on all $k$-separable states, and being strictly greater than zero for all $k$-nonseparable states. In particular, the $q\text{\ensuremath{-}}\mathrm{2}\text{\ensuremath{-}}\mathrm{ME}$ concurrence and $\ensuremath{\alpha}\text{\ensuremath{-}}2\text{\ensuremath{-}}\mathrm{ME}$ concurrence, renamed as $q\text{\ensuremath{-}}\mathrm{GME}$ concurrence and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{GME}$ concurrence, respectively, are two kinds of genuine entanglement measures corresponding to the case where the systems are divided into bipartition $(k=2)$. The lower bounds of the two classes $k$-nonseparable measures are obtained by employing the approach that tak...