Moments based entanglement criteria and measures

Abstract

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great signiffcance to ffnd efffcient and experimentally friend separability criteria to detect entanglement. In this paper, we ffrstly propose two easily used entanglement criteria based on matrix moments. The ffrst entanglement criterion only uses the ffrst two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more ffne ways than the existing measures.