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arXiv · 2503.14245

Parameterized bipartite entanglement measures and entanglement constraints

Wen Zhou·Zhong-Xi Shen·Dong-Ping Xuan·Zhi-Xi Wang·Shao-Ming Fei
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Abstract

In this paper, we propose a novel class of parameterized entanglement measures which are named as $G_\omega$-concurrence ($G_\omega$C) ($0<\omega\leq1$), and demonstrate comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, we derive an analytical formula relating $G_\omega$C to concurrence for the range of $0.85798\leq\omega\leq1$ within two-qubit systems. Additionally, we prove a new polygamy relation of multiqubit quantum entanglement in terms of $G_\omega$-concurrence of assistance ($G_\omega$CoA). However, it fails to obey the monogamy relation, but we have demonstrated that the squared $G_\omega$-concurrence (S$G_\omega$C) does obeys a general monogamy relation in an arbitrary $N$-qubit mixed state. Based on the monogamy properties of S$G_\omega$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$G_\omega$C still has the applicability of the monogamy relation.

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Wen Zhou, Zhong-Xi Shen, Dong-Ping Xuan, Zhi-Xi Wang, Shao-Ming Fei. 2025-03-18. Parameterized bipartite entanglement measures and entanglement constraints. https://doi.org/10.1002/qute.202400707

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