followed by a local measurement on the probe, yields identical information as single-mode illumination. For CV illumination, this is only approximately true; these two quantities approach equality in the limit of low reflectivity and low probe energy.

Finally, in DV illumination, the consumed discord is exactly equal to the Holevo information quantum advantage and the accessible information quantum advantage. We found, for CV illumination, that this approximately holds for the Holevo information, but not for the accessible information. The differences between DV and CV illumination are summarized in Table \[table1\].

Conclusion {#sec_conclusion}
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![ One million small perturbations were made on a coherent state. This is a histogram of the Holevo information when the top 500 000 states are used in single-mode illumination. The vertical line shows the Holevo information of the coherent state. Parameters are $n_{\rm env}=4$, $\epsilon=0.5$, $\bar n=0.5$. []{data-label="fig_perturbed"}](perturbedcoherent.pdf){width="8.6cm"}

In [@weedbrook2016discord], it has been shown that quantum discord coincides exactly with quantum advantage in a DV quantum illumination. Here, we complete the picture by extending the framework to CV quantum illumination [@PhysRevLett.101.253601]. To this end, we numerically calculated the performance enhancement that quantum illumination has over single-mode illumination and compared it to the Gaussian discord of the 