Optimal indecomposable witnesses without extremality as well as spanning   property
  One of the interesting problems on optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable witness which neither has the spanning property nor is associated with extremal positive linear map. Here, we answer this question negatively by examining the extremality of the positive linear maps constructed by Qi and Hou [J. Phys. A {\bf 44}, 215305 (2100)]. 
Kil-Chan Ha and Hoseog Yu
quant-ph math-ph math.MP math.OA