CAJ | 학술논문

为了得出一类密度矩阵的可分判据研究了特殊图,利用图理论、拉普拉斯矩阵性质、部分转置正判据、图上顶点与其部分转置图上对应顶点之间的度数关系,分别给出了完全纠缠( perfect entangled,PE)匹配图在Cp Cq与C3 C4量子系统中的可分判据。证明了在Cp Cq量子系统中,若n=pq个顶点上的PE-匹配图的部分转置不是PE-匹配的,则该图的密度矩阵是纠缠的,否则其部分转置是非负( positive partial transpose,PPT)的；并给出了C3 C4系统中n=3×4个顶点上的PE-匹配图的密度矩阵可分的充要条件是该图的部分转置也是PE-匹配图。
위료득출일류밀도구진적가분판거연구료특수도,이용도이론、랍보랍사구진성질、부분전치정판거、도상정점여기부분전치도상대응정점지간적도수관계,분별급출료완전규전( perfect entangled,PE)필배도재Cp Cq여C3 C4양자계통중적가분판거。증명료재Cp Cq양자계통중,약n=pq개정점상적PE-필배도적부분전치불시PE-필배적,칙해도적밀도구진시규전적,부칙기부분전치시비부( positive partial transpose,PPT)적；병급출료C3 C4계통중n=3×4개정점상적PE-필배도적밀도구진가분적충요조건시해도적부분전치야시PE-필배도。
The separable criterion of a class of density matrix is presented by studying a special graph. Using graph theory, the property of Laplacian matrix, the positive partial transpose criterion and the relationship of degree between the vertices of graph and the corresponding vertices of partial transpose of the graph, the separable criterion of PE-matching graph in Cp Cq and C3 C4 is given respectively. In Cp Cq quantumsystems, It is proven that if the partial transpose of a PE-matching graph on n = pq verticesis not a PE-matching, thedensity matrix of this graph is entanglement, otherwise it is PPT ( positive partial transpose ) . It is also presented that in C3 C4 systems if the density matrix of PE-matching graph on n=3 × 4 vertices is separable, the necessary and sufficient condition is that the partial transpose of this graph is also a PE-matching graph.