approaches zero when $\epsilon\to0$. Since $\delta^{\rm G}_{\rm con}({\rm A}|{\rm B})=\chi_q-\chi_c$, this leads us to the conclusion that in the limit of low reflectivity and low probe energy, $\chi_q-\chi_s$ converges to the Gaussian discord consumed. Hence, discord encoded can suitably explain the quantum advantage of quantum illumination, if quantum illumination is viewed as a communication problem with access to devices such as quantum memory.

On the other hand, $A_q-A_s$, which quantifies the performance advantage for quantum illumination in the single-copy measurement case, is more relevant from a practical point of view since this does not require the storage of quantum states [@SHGSC16]. From Fig. \[fig\_plot02\], we see that $\delta^{\rm G}_{\rm con}({\rm A}|{\rm B})$ is greater than $A_q-A_s$ and $A_q-A_c$. This discrepancy is mainly due to the difference between the Holevo information $\chi_q$ and the accessible information $A_q$ for the states involved in quantum illumination. Hence, measuring each illumination event separately does not fully harness the benefits offered by the discord. However, it is sufficient to provide some quantum advantage over single-mode illumination.

Quantum advantage versus probe energy
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![ The accessible information and Holevo information quantities (top) and consumed Gaussian discord and quantum advantage (bottom) vs the mean energy of the 