一扇许可的概括的量门(介绍了由长,刘和王) 有 U = k=0 d 的形式 ? 1 c k U k,在 U ks 是单一的的地方 Hilbert 上的操作员空间 H 并且|k=0 d ? 1 c k |? 1 并且 | c k |? 1 (0 ? k ? d ? 1 ) 。在我们考虑一种 AGQG 的这个工作,打电话给限制的许可的概括的量门(RAGQG ) ,令人满意 0 < k=0 d ? 1 | c k |? 1。H 上的所有 RAGQG 的集合 RAGQG (H) 的一些性质被建立。特别,我们证明 RAGQG (H) 的极端点确切是 H 和那 B (H)=R + RAGQG (H) 上的单一的操作员。
An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of U = ∑k=0^d-t ckUk, where Uk's are unitary operators on a Hilbert space H and |U = ∑k=0^d-t ck|≤1 and |Ck|≤1(0≤d≤k-1). In this work we consider a kind of AGQGs,called restricted allowable generalized quantum gates (RAGQGs), satisfying 0 〈 |U = ∑k=0^d-t ck|≤1. Some properties of the set RAGQG(H) of all RAGQGs on H are established. Especially, we prove that the extreme points of RAGQG(H) are exactly unitary operators on H and that B(H)=R+RAGQG(H).