ic ist ▁Ar un ▁K . ▁P ati ▁along ▁with ▁ ▁Samuel ▁L . ▁Braun stein ▁proved ▁this ▁theorem . ▁ ▁The ▁no - de let ing ▁theorem , ▁together ▁with ▁the ▁no - cl oning ▁theorem , ▁under pin ▁the ▁interpretation ▁of ▁quantum ▁mechan ics ▁in ▁terms ▁of ▁category ▁theory , ▁and , ▁in ▁particular , ▁as ▁a ▁d agger ▁symmetric ▁mon oid al ▁category . ▁This ▁form ulation , ▁known ▁as ▁categor ical ▁quantum ▁mechan ics , ▁in ▁turn ▁allows ▁a ▁connection ▁to ▁be ▁made ▁from ▁quantum ▁mechan ics ▁to ▁linear ▁logic ▁as ▁the ▁logic ▁of ▁quantum ▁information ▁theory ▁( in ▁exact ▁anal ogy ▁to ▁classical ▁logic ▁being ▁founded ▁on ▁Cart esian ▁closed ▁categories ). ▁ ▁Over view ▁of ▁quantum ▁delet ion ▁Suppose ▁that ▁there ▁are ▁two ▁copies ▁of ▁an ▁unknown ▁quantum ▁state . ▁A ▁pert inent ▁question ▁in ▁this ▁context ▁is ▁to ▁ask ▁if ▁it ▁is ▁possible , ▁given ▁two ▁identical ▁copies , ▁to ▁delete ▁one ▁of ▁them ▁using ▁quantum ▁mechanical ▁operations ? ▁It ▁turns ▁out ▁that ▁one ▁cannot . ▁The ▁no - de let ing ▁theorem ▁is ▁a ▁consequence ▁of ▁linear ity ▁of ▁quantum ▁mechan ics . ▁Like ▁the ▁no - cl oning ▁theorem ▁this ▁has ▁important ▁imp lications ▁in ▁quantum ▁computing , ▁quantum ▁information ▁theory ▁and ▁quantum ▁mechan ics ▁in ▁general . ▁ ▁The ▁process ▁of ▁quantum ▁deleting ▁takes ▁two ▁copies ▁of ▁an ▁arbitrary , ▁unknown ▁ ▁quantum ▁state ▁at ▁the ▁input ▁port ▁and ▁outputs ▁a ▁blank ▁state ▁along ▁with ▁the ▁original . ▁Mathemat ically , ▁ ▁this