caa a22 4500 475839536 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1023/A:1006317508252 doi (NATIONALLICENCE)springer-10.1023/A:1006317508252 On Bures Distance and *-Algebraic Transition Probability between Inner Derived Positive Linear Forms over W*-Algebras [Elektronische Daten] [Peter Alberti, Armin Uhlmann] On a W*-algebra M, for given two positive linear forms ν,ρ∈ M + * and algebra elements a, b ∈ M, a variational expression for the Bures distance d B(ν a , ϱ b ) between the inner derived positive linear forms ν a =ν(a *·a) and ρ b =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 'sweak intertwiners", in algebraic quantum field theory. In the last section, some optimization problem will be considered. Kluwer Academic Publishers, 2000 W*-algebras nationallicence positive linear forms nationallicence Bures distance nationallicence inner operations nationallicence Alberti Peter Institute of Theoretical Physics, University of Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany. e-mail aut Uhlmann Armin Institute of Theoretical Physics, University of Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany. e-mail aut Acta Applicandae Mathematica Kluwer Academic Publishers 60/1(2000-01-01), 1-37 0167-8019 60:1<1 2000 60 10440 https://doi.org/10.1023/A:1006317508252 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1006317508252 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alberti Peter Institute of Theoretical Physics, University of Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany. e-mail aut NATIONALLICENCE 700 1- Uhlmann Armin Institute of Theoretical Physics, University of Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 60/1(2000-01-01), 1-37 0167-8019 60:1<1 2000 60 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer