  Entangled states, like the two-mode squeezed vacuum state, are known to give
quantum advantage in the illumination protocol, a method to detect a weakly
reflecting target submerged in a thermal background. We use non-Gaussian
photon-added and -subtracted states, affected by local Gaussian noise on top of
the omnipresent thermal noise, as probes in the illumination protocol. Based on
the difference between the Chernoff bounds obtained with the coherent state and
the non-Gaussian state having equal signal strengths, whose positive values
denote quantum advantage in illumination, we highlight the hierarchy among
non-Gaussian states, which is compatible with correlations per unit signal
strength, although the Gaussian states offer the best performance.
Interestingly, such hierarchy is different when comparisons are made using the
Chernoff bounds. The entire analysis is performed in the presence of different
imperfect apparatus like faulty twin-beam generator, imperfect photon addition
(subtraction) as well as with noisy non-Gaussian probe states.
