Efficient k-separability criteria for mixed multipartite quantum states

¹ College of Mathematics and Information Science, Hebei Normal University - Shijiazhuang 050024, China
² State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University Beijing 100084, China
³ College of Physics Science and Information Engineering, Hebei Normal University - Shijiazhuang 050024, China

^(a) gaoting@hebtu.edu.cn
^(b) flyan@hebtu.edu.cn

Received: 1 April 2013
Accepted: 21 October 2013

Abstract

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient k-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish n − 1 different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti-W states, and mixtures thereof. They detect k-nonseparable n-partite quantum states which have previously not been identified. Here . No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most local measurements.