  In Quantum Illumination (QI), a signal beam initially entangled with an idler
beam held at the receiver interrogates a target region bathed in thermal
background light. The returned beam is measured jointly with the idler in order
to determine whether a weakly reflecting target is present. Using tools from
quantum information theory, we derive lower bounds on the average error
probability of detecting both specular and fading targets and on the mean
squared error of estimating the reflectance of a detected target, which are
obeyed by any QI transmitter satisfying a signal energy constraint. For bright
thermal backgrounds, we show that the QI system using multiple copies of
low-brightness two-mode squeezed vacuum states is nearly optimal. More
generally, our results place limits on the best possible performance achievable
using QI systems at all wavelengths, and at all signal and background noise
levels.
