Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form
Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form
复制标题
乌尔曼转移概率与标准形式冯·诺依曼代数自然正锥导出的转移概率的比较
DOI：
10.1007/bf00403277
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发表时间：
1982
影响因子：
1.2
通讯作者：
G. A. Raggio
中科院分区：
文献类型：
--
作者：
G. A. Raggio
证明了对于W *-代数的正规态ρ和φ，其中P（.，.）是Uhlmann [1]所考虑的转移概率，而ω（ω）是与正常状态ω相关联的A的某个标准忠实表示的自然正锥中的向量。上面的不等式等价于：$$d（\rho，\phi）\leqslant||\xi（\rho）- \xi（\phi）||倾斜 \leqslant d（\rho，\phi）（2（1 - \frac{1}{4}d（\rho，\phi）^2））^{1/2} \leqslant 2^{1/2} d（\rho，\phi）$$，其中（.，.）是Bures距离函数[5]。
It is shown that for normal states ρ and φ of aW*-algebra, whereP(.,.) is the transition probability considered by Uhlmann [1], and ζ(ω) is the vector in the natural positive cone of some standard faithful representation ofA, associated with the normal state ω. The above inequality is equivalent to: $$d(\rho ,\phi ) \leqslant ||\xi (\rho ) - \xi (\phi )|| \leqslant \leqslant d(\rho ,\phi )(2(1 - \frac{1}{4}d(\rho ,\phi )^2 ))^{1/2} \leqslant 2^{1/2} d(\rho ,\phi )$$ , whered(.,.) is the Bures distance function [5].