CB-norm estimates for maps between noncommutative \(L_{p}\)-spaces and quantum channel theory (Q2796767)

This work aims, by means of using quantum teleportation, one of the most important quantum information protocols, to provide some very sharp embeddings between noncommutative \(L_p\)-spaces. Some type of embeddings is given in Theorem 1.1 that is used to study the type and cotype or \(K\)- and \(B\)-convexities in the context of operator spaces. Moreover, the Corollary 1.2 of this Theorem provides a very tight estimate for the dimension of the noncommutative part (\(S_q\)-space). Applying the ideas from the superdense coding, another important protocol of quantum information, the authors also prove Theorem 1.3 that can be understood as a complement of Theorem 1.1. Further, analyzing the quantum depolarizing channel, two parts of Theorems 1.4 and 1.6 that correspond to this channel are proved. Another parts of these theorems are proved in Section 5 that examines the quantum erasure channel. The latter capacity is then computed and some noncommutative results are demonstrated for the quantum depolarizing channel.