Entanglement hierarchies in multipartite scenarios
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912291358769152 |
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| author | Li, Hui Gao, Ting Yan, Fengli |
| author_facet | Li, Hui Gao, Ting Yan, Fengli |
| contents | In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite entanglement measures and allow for fine identification among distinct entanglement contributions. This kind of quantifications, termed $k$-GM concurrence, can unambiguously classify entangled states into $(n-1)$ distinct classes from the perspective of $k$-nonseparability with $k$ running from $n$ down to 2, and comply with the axiomatic conditions of an entanglement measure. Compared to $k$-ME concurrence [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062323} {Phys. Rev. A \textbf{86}, 062323 (2012)}], the hierarchical measures proposed by us embody advantages in distinguishing same class entangled state and measuring continuity. In addition, we establish the relation between $k$-ME concurrence and $k$-GM concurrence, and further derive a strong lower bound on the $k$-GM concurrence by exploiting the permutationally invariant part of a quantum state. Furthermore, we parametrize $k$-GM concurrence to obtain two more general and complete categories of quantifications, $q$-$k$-GM concurrence $(q>1)$ and $α$-$k$-GM concurrence $(0\leqα<1)$, which obey the properties enjoyed by $k$-GM concurrence as well. In particular, $α$-$2$-GM concurrence $(0<α<1)$ determines that the GHZ state and the $W$ state belong to the same hierarchy, and it is proven in detail satisfying the requirement that the GHZ state is more entangled than the $W$ state in multiqubit systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement hierarchies in multipartite scenarios Li, Hui Gao, Ting Yan, Fengli Quantum Physics In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite entanglement measures and allow for fine identification among distinct entanglement contributions. This kind of quantifications, termed $k$-GM concurrence, can unambiguously classify entangled states into $(n-1)$ distinct classes from the perspective of $k$-nonseparability with $k$ running from $n$ down to 2, and comply with the axiomatic conditions of an entanglement measure. Compared to $k$-ME concurrence [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062323} {Phys. Rev. A \textbf{86}, 062323 (2012)}], the hierarchical measures proposed by us embody advantages in distinguishing same class entangled state and measuring continuity. In addition, we establish the relation between $k$-ME concurrence and $k$-GM concurrence, and further derive a strong lower bound on the $k$-GM concurrence by exploiting the permutationally invariant part of a quantum state. Furthermore, we parametrize $k$-GM concurrence to obtain two more general and complete categories of quantifications, $q$-$k$-GM concurrence $(q>1)$ and $α$-$k$-GM concurrence $(0\leqα<1)$, which obey the properties enjoyed by $k$-GM concurrence as well. In particular, $α$-$2$-GM concurrence $(0<α<1)$ determines that the GHZ state and the $W$ state belong to the same hierarchy, and it is proven in detail satisfying the requirement that the GHZ state is more entangled than the $W$ state in multiqubit systems. |
| title | Entanglement hierarchies in multipartite scenarios |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.01014 |