  Quantum measurements are basic operations that play a critical role in the
study and application of quantum information. We study how the use of quantum,
coherent, and classical thermal states of light in a circuit quantum
electrodynamics setup impacts the performance of quantum measurements, by
comparing their respective measurement backaction and measurement signal to
noise ratio per photon. In the strong dispersive limit, we find that thermal
light is capable of performing quantum measurements with comparable efficiency
to coherent light, both being outperformed by single-photon light. We then
analyze the thermodynamic cost of each measurement scheme. We show that
single-photon light shows an advantage in terms of energy cost per information
gain, reaching the fundamental thermodynamic cost.
