On Bures Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebras
On Bures Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebras
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关于W*-代数上内导正线性形式之间的Bures距离和*-代数转移概率
DOI：
10.1023/a:1006317508252
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
A. Uhlmann
中科院分区：
文献类型：
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作者：
P. M. Alberti;A. Uhlmann
在W*-代数M上，对给定的两个正线性形式ν，ρ∈M+* 和代数元素a，B∈M，得到了内导正线性形式νa=ν（a*·a）和ρB=ρ（B*·B）之间的Bures距离B（νa，B）的变分表达式.沿着公式的证明，也给出了S. Gudder关于非交换概率的定理将作略微的推广。此外，给出的Bures距离表达式与D.布赫霍尔茨，它发生在代数量子场论中，沿着估计所谓的“弱缠绕”的问题。在最后一节中，将考虑一些优化问题。
On a W*-algebraM, for given two positive linear forms ν,ρ∈M+*and algebra elementsa,b∈M, a variational expression for the Bures distancedB(νa, ϱb) between the inner derived positive linear forms νa=ν(a*·a) and ρb=ρ(b*·b) is obtained. Along with the proof of the formula, also an earlier result of S. Gudder on noncommutative probability will be slighly extended. Also, the given expression of the Bures distance relates nicely to the system of seminorms proposed by D. Buchholz which occurs, along with the problem of estimating the so-called `weak intertwiners", in algebraic quantum field theory. In the last section, some optimization problem will be considered.