Abstract
An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of U = Σ d−1k=0 c k U k , where U k’s are unitary operators on a Hilbert space H and |Σ d−1k=0 c k |⩽1 and |c k |⩽1 (0⩽k⩽d−1). In this work we consider a kind of AGQGs, called restricted allowable generalized quantum gates (RAGQGs), satisfying 0 < Σ d−1k=0 |c k |⩽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).
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Cao, H., Li, L., Chen, Z. et al. Restricted allowable generalized quantum gates. Chin. Sci. Bull. 55, 2122–2125 (2010). https://doi.org/10.1007/s11434-010-3221-5
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DOI: https://doi.org/10.1007/s11434-010-3221-5