▁of ▁an ▁unknown ▁qu bit . ▁ ▁If ▁we ▁have ▁two ▁copies ▁of ▁an ▁unknown ▁qu bit , ▁then ▁by ▁linear ity ▁of ▁the ▁deleting ▁transformation ▁we ▁have ▁▁ ▁In ▁the ▁above ▁expression , ▁the ▁following ▁transformation ▁has ▁been ▁used : ▁▁ ▁However , ▁if ▁we ▁are ▁able ▁to ▁delete ▁a ▁copy , ▁then , ▁at ▁the ▁output ▁port ▁of ▁the ▁deleting ▁machine , ▁the ▁combined ▁state ▁should ▁be ▁ ▁. ▁ ▁In ▁general , ▁these ▁states ▁are ▁not ▁identical ▁and ▁hence ▁we ▁can ▁say ▁that ▁the ▁machine ▁fails ▁to ▁delete ▁a ▁copy . ▁If ▁we ▁require ▁that ▁the ▁final ▁output ▁states ▁are ▁same , ▁then ▁we ▁will ▁see ▁that ▁there ▁is ▁only ▁one ▁option : ▁ ▁and ▁ ▁Since ▁final ▁state ▁ ▁of ▁the ▁anc illa ▁is ▁normal ized ▁for ▁all ▁values ▁of ▁ ▁it ▁must ▁be ▁true ▁that ▁ ▁and ▁ ▁are ▁orthogonal . ▁This ▁means ▁that ▁the ▁quantum ▁information ▁is ▁simply ▁in ▁the ▁final ▁state ▁of ▁the ▁anc illa . ▁One ▁can ▁always ▁obtain ▁the ▁unknown ▁state ▁from ▁the ▁final ▁state ▁of ▁the ▁anc illa ▁using ▁local ▁operation ▁on ▁the ▁anc illa ▁Hil bert ▁space . ▁Thus , ▁linear ity ▁of ▁quantum ▁theory ▁does ▁not ▁allow ▁an ▁unknown ▁quantum ▁state ▁to ▁be ▁deleted ▁perfectly . ▁ ▁Conse quence ▁ ▁If ▁it ▁were ▁possible ▁to ▁delete ▁an ▁unknown ▁quantum ▁state , ▁then , ▁using ▁two ▁pairs ▁of ▁E PR ▁states , ▁we ▁could ▁send ▁signals ▁faster ▁than ▁light . ▁Thus , ▁viol ation ▁of ▁the ▁no - de let ing ▁theorem