paper

G_q-concurrence and entanglement constraints in multiqubit systems

arXiv:2406.19080

Abstract

In this paper, we introduce a category of one-parameter bipartite entanglement quantifiers, termed $G_{q}$ -concurrence ( $q > 1$ ), and show rigorously that they satisfy all the axiomatic conditions of an entanglement measure and can be considered as a generalization of concurrence. In addition, we establish an analytic formula relating $G_{q}$ -concurrence to concurrence for $1 < q \leq 2$ in two-qubit systems. Furthermore, the polygamy relation is presented based on the $G_{q}$ -concurrence of assistance in multiqubit systems. As far as $G_{q}$ -concurrence ( $1 < q \leq 2$ ) itself is concerned, however, it does not obey the monogamy relation, but we prove that the square of $G_{q}$ -concurrence does. By means of this monogamy inequality, we construct a set of entanglement indicators that can detect genuinely multiqubit entangled states even when the tangle loses its efficacy.

11 pages, 7 figures