In this paper, we study the monogamy inequality of Tsallis $q$-entropy entanglement. We first provide an analytic formula of Tsallis $q$-entropy entanglement in two-qubit systems for $\frac{5-\sqrt{13}}{2}\le q\le \frac{5+\sqrt{13}}{2}.$ The analytic formula of Tsallis $q$-entropy entanglement in $2\otimes d$ system is also obtained and we show that Tsallis $q$-entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis $q$-entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.

• Received 2 May 2016

DOI:https://doi.org/10.1103/PhysRevA.93.062340