  A unified framework is proposed in this paper for parameter estimation using
convex optimization and experiment design applying convex maximization for
Pauli channels, that can be extended to generalized Pauli channels, too. In the
case of known channel directions, an affine parametrization of the Choi matrix
turns the LS parameter estimation into a convex optimization problem also for
the generalized Pauli channels. A simple iterative algorithm for estimating the
channel directions is also given for qubit Pauli channels.
  The experiment design was performed by maximizing the trace of the Fisher
information matrix of the output quantum system to find optimal input state and
measurement POVM for the channel estimation. For the known channel direction
case it was found that the optimal input state should be pure and the optimal
measurement POVM is extremal. It was also shown that both the input state and
the POVM elements in the optimal configuration should be parallel to the
channel directions in the qubit Pauli channel case.
  The proposed methods and algorithms are illustrated by simple numerical
examples.
