We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalize existing criteria. Each condition corresponds to a convex optimization problem which, given the covariance matrix of the state, can be numerically solved in a straightforward way. The conditions are independent of partial transposition and thus are also able to detect bound entangled states. Our approach can be used to obtain an analytical condition for genuine multipartite entanglement. We demonstrate that even a special case of our conditions can detect entanglement very efficiently. Using multiobjective optimization, it is also possible to numerically verify genuine entanglement of some experimentally realizable states.

• Received 29 April 2015
• Revised 3 July 2015

DOI:https://doi.org/10.1103/PhysRevA.92.042328