I introduce a quantum map formalism modeling two sources of measurement imperfection — particle-indexing errors and limited detector resolution — giving rise to fuzzy and coarse-grained quantum maps linked by a partial trace. A key result is that the volume of tomographically accessible states shrinks at a double-exponential rate in the number of particles. I then present a geometric and probabilistic characterization of the coarse-graining channel: the probability density over coarse-grained states concentrates sharply around the maximally mixed state as system size grows, making nearly pure coarse-grained states exponentially rare. Finally, using a maximum-entropy assignment map to invert the coarse-graining, I examine the effective dynamics induced by unitary microscopic evolution. The resulting dynamics are strikingly non-standard: nonlinear, non-Markovian, and initial-state dependent.