On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra

Details On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra On Bures-Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebra

2002-02-25

arxiv.org/abs/math-ph/0202038v1

Acta Applicandae Mathematicae, 60(1):1--37, 2000

Physics

Mathematical Physics

LaTeX2e (elsart), 40 pages

Scientific paper

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.

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