  An important step in quantum simulation is to measure the many-body
correlations of the simulated model. For a practical quantum simulator composed
of finite number of qubits and cavities, in contrast to ideal many-body systems
in the thermodynamic limit, a measurement device can generate strong backaction
on the simulator, which could prevent the accurate readout of the correlation
functions. Here we calculate the readout of a detector coupled to an analog
quantum simulator. We show that reliable characterization of the many-body
correlations in the simulator can be achieved when the coupling operators obey
the Wick's theorem. Our results are illustrated with two examples: a simulator
for an harmonic oscillator and a simulator for the free electron gas.
