Cloning and Broadcasting in Operator Algebras

Multicloning and Multibroadcasting in Operator Algebras

“…belonging to respective preduals. For an arbitrary subset of the normal states of A, it is shown that is multibroadcastable if and only if there is a countable family of normal states having mutually orthogonal supports such that each ρ ∈ is a convex combination of these states, generalizing thus a result obtained in [7] for the case of simple broadcasting. Moreover, it is shown that is multicloneable if and only if the states from it have mutually orthogonal supports, which again generalizes a similar result in [7].…”

“…Applying to K * our previous considerations, we obtain that F(S) is an abelian atomic von Neumann algebra. Now, the proof follows the lines of the proof of Theorem 3.10 in [7].…”

“…the setup where instead of the full algebra of all bounded operators on a finite-dimensional Hilbert space an arbitrary von Neumann algebra is considered, was investigated in [7], where also the assumption of complete positivity of the broadcasting (cloning) operation was weakened to the form of the so-called 1 1 2 -positivity, i.e. the operation being a Schwarz (or strongly positive) map.…”

“…the operation being a Schwarz (or strongly positive) map. The present paper aims at a generalization of some results from [7] to the multi-fold variant.…”

“…It should be noted that in this work we follow in many respects the basic ideas of [7], exploiting them in the multi-fold case.…”