We obtain hypercontractivity estimates for a large class of semigroups defined on finite-dimensional matrix algebras Mn. These semigroups arise from Poisson-like length functions Ψ on Zn × Zn and provide new hypercontractive families of quantum channels when Ψ is conditionally negative. We also study the optimality of our estimates.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics