to case 1, when both quantum and classical correlations are utilized.\
*Case 3*. Single-mode illumination: $A_s$ and $\chi_s$ are the accessible information and Holevo information, respectively, when Bob uses a single-mode coherent state with a fixed amplitude $\alpha$ as the illumination probe.\
The quantum advantage is defined as the difference between the performance of quantum illumination and single-mode illumination protocol. The protocols are compared for scenarios where the probe states have coinciding energy. This constraint allows for fair comparison, as it is always possible to detect the presence of an object with any fixed accuracy by using a sufficiently energetic probe. The quantum advantage in terms of accessible information is $A_q-A_s$ and the Holevo information quantum advantage is $\chi_q-\chi_s$, where each information quantity is evaluated over the probe with mean photon number $\bar n$. As we shall show in this paper, these quantum advantages can be linked to the discord consumed in the illumination protocol.

Discord and Quantum Illumination {#sec_discord}
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Quantum discord is a measure of the nonclassical correlations between two quantum states. It arises from the difference between quantum analogs of two distinct definitions of the classical mutual information [@0305-4470-34-35-315; @PhysRevLett.88.017901]: $$\begin{aligned}
I({\rm A}:{\rm B})&=S({\rm A})+S({\rm B})-S({\rm AB}) 