  We describe a unified framework of phase covariant multi user quantum
transformations for d-dimensional quantum systems. We derive the optimal phase
covariant cloning and transposition tranformations for multi phase states. We
show that for some particular relations between the input and output number of
copies they correspond to economical tranformations, which can be achieved
without the need of auxiliary systems. We prove a relation between the optimal
phase covariant cloning and transposition maps, and optimal estimation of
multiple phases for equatorial states.
