Parameterized bipartite entanglement measures and entanglement constraints

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.