Cloning and Broadcasting In Operator Algebras

kaniowski, krzysztof; lubnauer, katarzyna; Łuczak, andrzej;

We investigate cloning and broadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained so far in finite dimension, and for the full algebra of
operators on a Hilbert space. Moreover, we also weaken the assumption of complete positivity of the broadcasting (cloning) operation. It turns out that some results can be expressed in terms of
modular theory for W ∗-algebras, in particular, the Connes cocycles are used for a characterization of broadcastability.