L-Fuzzy伴随的若干特征定理照

研究 Frame格上的一类等价关系 ,给出 L - Fuzzy伴随的若干性质定理及其等价刻画 ,体现了L- Fuzzy伴随的层次伴随特点 ,最后引入广义 L-值偏序集的概念 ,得到了类似经典伴随的若干特征定理。     

一些量子结构的构造和Fuzzy有效空间

给出了Fuzzy有效空间的概念.利用偏序集上的特殊模糊子集构造了effect algebras,σ-effect algebras,orthoalgebras,orthomodular posets和σ-orthomodular posets.借助Fuzzy有效空间,得到了带有强序决定态系统的lattice effect algebras的一个表现定理.     

相通连续Domain的若干特征定理

首先引入了相通连续Domain的概念,利用主理想及连通闭集刻画了相通连续Domain; 其次考察了相通完备偏序集的定向完备化,得到了一些好的结果.     

Two-qubit pure state tomography by five product orthonormal bases

In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {|00 |,|1,1| }. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases {B_1,B_2,B_3}. Denote the unitary transition matrices from B_1 to {B_2,B_3 } as U1 and U2. All 32 elements of matrices U_1 and U_2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.     

极大点空间的若干特征定理

本文利用极大点空间的等价刻划证明了极大点空间的某些子空间、不交和、 乘积空间、逆序列的逆极限、具有可数基的局部紧的Hausdorff空间是极大点空间,还 给出了具有可数基的局部紧的Hausdorff空间的Domain hull.     

Z-连通集系统及其范畴特征

本文引入了Z-连通集系统的概念,讨论了Z-连通连续偏序集的一系列性 质,证明了Z-连通连续偏序集范畴对偶等价于完全分配格范畴的一个满子范畴.