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Convexity, unitary invariance and monotonicity under completely positive maps over injective vN-algebras

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Abstract

The action of dynamical maps over the normal state space of a properly infinite, injective vN-algebra is analyzed and shown to be equivalent to convec unitary mixing with respect to some suitably chosen C *-subalgebra. As an application, it is shown that the conditions usually imposed on (convex) relative state functionals (like the relative entropy etc.) necessarily imply their decrease under completely positive maps.

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  1. Sektion Mathematik und Naturwissenschaftlich-Theoretisches Zentrum (NTZ), Karl-Marx-Universität Leipzig, 7010, Leipzig, DDR

    Peter M. Alberti

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  1. Peter M. Alberti
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Alberti, P.M. Convexity, unitary invariance and monotonicity under completely positive maps over injective vN-algebras. Letters in Mathematical Physics 12, 249–256 (1986). https://doi.org/10.1007/BF00402657

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