Case 1: Two different optimizations in relation to quantum discord It is proved that quantum discord and its geometry measure can be rewritten as OD, (PAB)=S(PA)+minXp s(p8lia-S(PAB AB PAB DA(PAB)=min PAB -xaB AB AB Where IIi is the projector state achieving the minimize herefore we could choose the two projector states as our optimal bases, so that we could get some physics about dissipate process with different optimizations S.L. Luo andss Fu, PhysRevA. 82.034302Case 1: Two different optimizations in relation to quantum discord It is proved that quantum discord and its geometry measure can be rewritten as: Where is the projector state achieving the minimize. S.L. Luo and S.S. Fu,PhysRevA.82.034302 A i ( ) ( )   ( ) ( ) ( ) ( ) min A i A A AB A i B A AB i A A i i AB AB QD S p S i S I I        = + − = −    Therefore we could choose the two projector states as our optimal bases,so that we could get some physics about dissipate process with different optimizations. ( ) 0 2 2 min AB A AB AB AB A A i i AB AB D        = − = −  