Covariant Schwarz maps in M₂(ℂ)

Abstract We analyze a class of qubit maps displaying diagonal unitary and orthogonal symmetries. For unital maps we characterize all covariant maps satisfying an operator Schwarz inequality. In particular well known Pauli maps are completely characterized. Going beyond the unital case we consider recently proposed generalizations of Schwarz inequality and provide the corresponding necessary and sufficient conditions for the entire class of covariant maps.