On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra
Mathematical Physics
2015-11-18 v1 math.MP
Operator Algebras
Abstract
On a W*-algebra M, for given two positive linear forms f,g and algebra elements a,b a variational expression for the Bures-distance d_B(f^a,g^b) between the inner derived positive linear forms f^a=f(a* . a) and g^b=g(b* . b) is obtained. Along with the proof of the formula also some earlier result of S.Gudder on non-commutative probability will be slightly extended. Also, the given expression of the Bures-distance nicely relates to some system of seminorms proposed by D.Buchholz and which occured along with the problem of estimating the so-called `weak intertwiners' in algebraic quantum field theory. In the last part some optimization problem will be considered.
Cite
@article{arxiv.math-ph/0202038,
title = {On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra},
author = {Peter M. Alberti and Armin Uhlmann},
journal= {arXiv preprint arXiv:math-ph/0202038},
year = {2015}
}
Comments
LaTeX2e (elsart), 40 pages