Geometric measure of entanglement of multipartite mixed states
  The geometric measure of entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with respect to this measure by a system of equations. The entanglement eigenvalue for a mixed state is introduced. For a given mixed state, we show that its nearest disentangled mixed state is associated with its entanglement eigenvalue. 
Shenglong Hu, Liqun Qi, Yisheng Song, Guofeng Zhang
quant-ph