Parameterized bipartite entanglement measures and entanglement constraints
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913743662743552 |
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| author | Zhou, Wen Shen, Zhong-Xi Xuan, Dong-Ping Wang, Zhi-Xi Fei, Shao-Ming |
| author_facet | Zhou, Wen Shen, Zhong-Xi Xuan, Dong-Ping Wang, Zhi-Xi Fei, Shao-Ming |
| contents | In this paper, we propose a novel class of parameterized entanglement measures which are named as $G_ω$-concurrence ($G_ω$C) ($0<ω\leq1$), and demonstrate comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, we derive an analytical formula relating $G_ω$C to concurrence for the range of $0.85798\leqω\leq1$ within two-qubit systems. Additionally, we prove a new polygamy relation of multiqubit quantum entanglement in terms of $G_ω$-concurrence of assistance ($G_ω$CoA). However, it fails to obey the monogamy relation, but we have demonstrated that the squared $G_ω$-concurrence (S$G_ω$C) does obeys a general monogamy relation in an arbitrary $N$-qubit mixed state. Based on the monogamy properties of S$G_ω$C, we can construct the corresponding multipartite entanglement indicators, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. In addition, for multipartite higher-dimensional systems, it is illustrated that S$G_ω$C still has the applicability of the monogamy relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameterized bipartite entanglement measures and entanglement constraints Zhou, Wen Shen, Zhong-Xi Xuan, Dong-Ping Wang, Zhi-Xi Fei, Shao-Ming Quantum Physics In this paper, we propose a novel class of parameterized entanglement measures which are named as $G_ω$-concurrence ($G_ω$C) ($0<ω\leq1$), and demonstrate comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, we derive an analytical formula relating $G_ω$C to concurrence for the range of $0.85798\leqω\leq1$ within two-qubit systems. Additionally, we prove a new polygamy relation of multiqubit quantum entanglement in terms of $G_ω$-concurrence of assistance ($G_ω$CoA). However, it fails to obey the monogamy relation, but we have demonstrated that the squared $G_ω$-concurrence (S$G_ω$C) does obeys a general monogamy relation in an arbitrary $N$-qubit mixed state. Based on the monogamy properties of S$G_ω$C, we can construct the corresponding multipartite entanglement indicators, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. In addition, for multipartite higher-dimensional systems, it is illustrated that S$G_ω$C still has the applicability of the monogamy relation. |
| title | Parameterized bipartite entanglement measures and entanglement constraints |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.14245 |