  In the quest for robust and universal quantum devices, the notion of
simulation plays a crucial role, both from a theoretical and from an applied
perspective. In this work, we go beyond the simulation of quantum channels and
quantum measurements, studying what it means to simulate a collection of
measurements, which we call a multimeter. To this end, we first explicitly
characterize the completely positive transformations between multimeters.
However, not all of these transformations correspond to valid simulations, as
evidenced by the existence of maps that always prepare the same multimeter
regardless of the input, which we call trash-and-prepare. We give a new
definition of multimeter simulations as transformations that are
triviality-preserving, i.e., when given a multimeter consisting of trivial
measurements they can only produce another trivial multimeter. In the absence
of a quantum ancilla, we then characterize the transformations that are
triviality-preserving and the transformations that are trash-and-prepare.
Finally, we use these characterizations to compare our new definition of
multimeter simulation to three existing ones: classical simulations,
compression of multimeters, and compatibility-preserving simulations.
