G_q-concurrence and entanglement constraints in multiqubit systems

TL;DR

This paper introduces a new family of entanglement measures called $G_q$-concurrence, establishes their properties, and explores their implications for multiqubit entanglement constraints and detection.

Contribution

It defines $G_q$-concurrence as a generalized entanglement measure, derives its relation to concurrence, and investigates its monogamy and polygamy properties in multiqubit systems.

Findings

$G_q$-concurrence satisfies entanglement measure axioms.

Analytic relation between $G_q$-concurrence and concurrence for $1<q extless 2$.

Constructed entanglement indicators for multiqubit states.

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 $1<q\leq2$ 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 ($1<q\leq2$) 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.