We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z2n). It acts in a natural way on the coordinates of the non-commutative 2-torus, T2n and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The class of operators may also be usefu...

The quantum speed of evolution for the phase covariant map is investigated. This involves absorption, emission and dephasing processes. We consider maps under various combinations above processes to investigate effect on limit time. For absorption-free maps, dissipative CP-(in)divisible (non)-Markovian noises are considered. role coherence-mixedness balance time checked in presence both vacuum ...