Upper bound of the fully entangled fraction
  We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled fraction of two qubits in a three-qubit mixed state has been also presented. 
Ming Li, Shao-Ming Fei, and Zhi-Xi Wang