Parameterized bipartite entanglement measures and entanglement constraints

Abstract

In this paper, we propose a novel class of parameterized entanglement measures which are named as $G_{\omega }$-concurrence ($G_{\omega }$C) ($0<\omega \le 1$), 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 $0.85798\le \omega \le 1$ 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.

11 pages, 15 figures

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