  We use symmetric measurement operators to construct quantum channels that
provide a further generalization of generalized Pauli channels. The resulting
maps are bistochastic but in general no longer mixed unitary. We analyze their
important properties, such as complete positivity and the ability to break
quantum entanglement. In the main part, we consider the corresponding open
quantum systems dynamics with time-local generators. From divisibility
properties of dynamical maps, we derive sufficient Markovianity and
non-Markovianity conditions. As instructive examples, we present the generators
of P-divisible generalized Pauli dynamical maps that allow for more negativity
in the decoherence rates.
