Completely Bounded Maps and Operator Algebras: Arveson's Extension Theorems

330 citations recorded by the source corpus.

Citations in the corpus

Gaussian quantum information (2011, neutral): “e channel is given by tracing out the environment after interaction, i.e., E(ˆρ) = TrE U(ˆρ⊗|ΦihΦ|E)U† . (107) An importantpropertyofthe Stinespringdilationis its uniqueness up to partial isometries (Paulsen, 2002). As a result, one can always choose |ΦiE = |0iE, where |0iE is a multimode vacuum sta”
Dilations, inclusions of matrix convex sets, and completely positive maps (2016, neutral): “, w(M)} with values in Mm(C) where m ≤ nM (the bound on the dimension m on which the spectral measure E acts follows from the proof of Naimark’s theorem via Stinespring’s theorem — see Chapter 4 of [23]).”
Quantum channels with memory (2005, neutral): “As a measure of the distance between two channels we favor the norm of complete boundedness , (or cb-norm , for short) [29], denoted by · cb . k For two channels T and S , the distance k T − S k cb can be deﬁned as the largest diﬀer-ence between the overall probabilities in two statistical quantum…”
The implicit function theorem and free algebraic sets (2014, neutral): “By a result of R. Smith [18], [13, Prop.”
ABOUT THE QWEP CONJECTURE (2003, neutral): “A general reference for the positive maps is Sections 2 and 3 in Paulsen’s book [ Pa1 ].”