QLunch: Elias Theil

Speaker: Elias Theil

Title: Unitary equivariant & permutation symmetric channels

Abstract: Many problems in quantum information theory have inherent symmetries. Two very prominent symmetries are unitary equivariance, which corresponds to a change of local basis for the problem, and permutation symmetry, which corresponds to a permutation of the individual inputs / outputs. Examples that display both of these symmetries are state cloning, purity amplification and (permutation) symmetrization of a state. In this talk, I will discuss unitary equivariant & permutation symmetric channels, give a classification of the extremal channels of this type and provide efficient (poly(m,n,d)) algorithms for their implementation in specific cases.