The Local Orthogonality between Quantum States and Entanglement   Decomposition
  In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki [Acta Phys. Slov. 48, 141 (1998).]. But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence. 
Sunho Kim, Junde Wu, Lin Zhang, Minhyung Cho
quant-ph