  We consider the problem of estimating unknown transmittance $\theta$ of a
target bathed in thermal background light. As quantum estimation theory yields
the fundamental limits, we employ the lossy thermal-noise bosonic channel
model, which describes sensor-target interaction quantum mechanically in many
practical active-illumination systems (e.g., using emissions at optical,
microwave, or radio frequencies). We prove that quantum illumination using
two-mode squeezed vacuum (TMSV) states asymptotically achieves minimal quantum
Cram\'{e}r-Rao bound (CRB) over all quantum states (not necessarily Gaussian)
in the limit of low transmitted power. We characterize the optimal receiver
structure for TMSV input, and show its advantage over other receivers using
both analysis and Monte Carlo simulation.
