Criterion for detection of genuine multipartite continuous-variable entanglement

In the multipartite systems there exist different types of entanglement where genuine entanglement is an important one. Due to its importance in quantum information tasks, various criteria have been presented for the detection of genuine entanglement. One of them is the criterion introduced by Shchukin et al. [E. Shchukin and P. van Loock, Phys. Rev. A 92, 042328 (2015)]. First they established an inequality such that any multipartite continuous-variable quantum state violating the inequality for any bipartition is genuine entangled. Since application of the inequality requires numerical optimization and becomes more difficult by increasing the number of parties, next by using the inequality they presented a single analytical condition for genuine entanglement which, although is not the best possible one, does not have these difficulties. In this paper, using the original inequality, we present a single analytical condition for genuine entanglement whose lower bound is greater than the lower bound of the analytical condition obtained by them and so it is able to detect more genuine entangled states. Moreover, it has the same detection ability as the original inequality without having its difficulties. We illustrate this through an example.