Hypercontractivity in finite-dimensional matrix algebras

摘要

We obtain hypercontractivity estimates for a large class of semigroups defined on finite-dimensional matrix algebras M-n. These semigroups arise from Poisson-like length functions Psi on Z(n) x Z(n) and provide new hypercontractive families of quantum channels when Psi is conditionally negative. We also study the optimality of our estimates. (C) 2015 AIP Publishing LLC.