▁ ▁and ▁. ▁Here ▁both ▁ ▁and ▁ ▁are ▁not ▁assumed ▁to ▁be ▁mut ually ▁orthogonal . ▁There ▁will ▁be ▁two ▁corresponding ▁pur ifications ▁of ▁the ▁mixed ▁state ▁ ▁reading ▁as ▁follows : ▁ ▁Pur ification ▁ 1 : ▁; ▁ ▁Pur ification ▁ 2 : ▁. ▁ ▁The ▁sets ▁and ▁ ▁are ▁two ▁collections ▁of ▁orth on ormal ▁bases ▁of ▁the ▁respective ▁auxili ary ▁spaces . ▁These ▁two ▁pur ifications ▁only ▁differ ▁by ▁a ▁unit ary ▁transformation ▁acting ▁on ▁the ▁auxili ary ▁space , ▁viz ., ▁there ▁exists ▁a ▁unit ary ▁matrix ▁such ▁that ▁. ▁Therefore , ▁, ▁where ▁means ▁that ▁we ▁can ▁realize ▁the ▁different ▁ens emb les ▁of ▁a ▁mixed ▁state ▁just ▁by ▁choosing ▁to ▁measure ▁different ▁observ ables ▁of ▁one ▁given ▁pur ification . ▁ ▁References ▁▁ ▁Category : Quant um ▁information ▁theory <0x0A> </s> ▁The ▁Pas por ▁Or ang ▁As ing ▁is ▁an ▁al ien ' s ▁pass port ▁issued ▁by ▁Indones ia . ▁It ▁is ▁a ▁two - year , ▁ 2 4 - page ▁document ▁issued ▁to ▁persons ▁perman ently ▁resident ▁in ▁Indones ia ▁who ▁cannot ▁obtain ▁travel ▁documents ▁from ▁any ▁other ▁country . ▁It ▁is ▁referred ▁to ▁in ▁English ▁various ly ▁as ▁" Ind ones ian ▁Pass port ▁for ▁Ali ens ", ▁" Ind ones ian ▁Stat eless ▁Person ▁Pass port ", ▁or ▁" Ind ones ian ▁Stat eless ▁Tra vel ▁Document ". ▁ ▁Details ▁The ▁ 1 9 5 0 ▁Tra vel ▁Document s ▁Act ▁used ▁the ▁term ▁" P as por ▁Or ang