A Sub-sequential Effect Algebra From The Quantum Programming Theory

In recent years,quantum information as an interdisciplinary subject such as mathematics,physics and computer science,has been one of the famous research fields.Hilbert space sequence effect algebra ?(H)is an important sequence effect algebra model,and the standard sequence product defined on it:A(?)B= A1/2BA1/2 is an important basic concept in quantum measurement theory.Hilbert space effect algebra occupies an important position in quantum science,which is the set of positive operators between 0 and the identity.This paper introduces a kind of sub-sequential effect algebra ?M(H)={T ?[0,M]:M E ?(H)} based on quantum programming theory,and discusses the new associative law of sequence products on it.Finally we found that due to the difference in algebraic structure,this new type of sequence effect algebra is very different from the existing nature of the effect algebra.The main conclusions in the article are as follows:If A,B ? then the following(a),(b),(c),(d)are equivalent to each other:(a)A(?)(C(?)B)=(A(?)C)(?)B for every C??M(H);(b)C(?)(A(?)B)=(C(?)A)(?)B for every C??m(H);(c)<A(?)Bx,x>=<Ax,x><Bx,x)for every x ? and ?x?=1;(d)A=?PM or B=?PM,where 0 ??,??1.