Physics – Quantum Physics
Scientific paper
2004-09-26
Lin. Alg. Appl. 404, 367-379 (2005).
Physics
Quantum Physics
results extended to some infinite dimensional cases, including the Gaussian bosonic channel
Scientific paper
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that the entries of a matrix representative of the map are non-negative (EP). In particular, for integer t, multiplicativity holds for the maximal 2 -> 2t norm of a product of two maps, whenever one of the pair is EP; for the maximal 1 -> t norm for pairs of CP maps when one of them is also EP; and for the maximal 1 -> 2t norm for the product of an EP and a 2-positive map. Similar results are shown in the infinite-dimensional setting of convolution operators on L^2(R), with the pointwise positivity of an integral kernel replacing entrywise positivity of a matrix. These results apply in particular to Gaussian bosonic channels.
King Christopher
Nathanson Michael
Ruskai Mary Beth
No associations
LandOfFree
Multiplicativity properties of entrywise positive maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multiplicativity properties of entrywise positive maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiplicativity properties of entrywise positive maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-448097