Enhanced quantum illumination of a lossy target: A sequential interaction model

Referee: §2 (Model): The SNR and QCB advantages for TMSS are derived under the assumption that the environment and target act as fully independent beam splitters receiving thermal inputs at different temperatures. No sensitivity analysis is provided for the equal-temperature case (target in equilibrium with surroundings), which would make the thermal inputs identical and alter the output covariance matrix; this is load-bearing for the claimed robustness and superiority.

Authors: The distinct-temperature assumption is physically motivated by scenarios in which the target has a different temperature from the surrounding environment, as is common in practical quantum illumination applications such as detecting warm objects. Nevertheless, we agree that including an analysis of the equal-temperature case enhances the discussion of robustness. In the revised manuscript, we have added a sensitivity analysis in Section 2. When the temperatures are equal, the thermal inputs to the two beam splitters are identical, resulting in a different output covariance matrix. Our additional calculations indicate that the TMSS still provides a higher SNR than the CS protocol in the low-reflectivity regime, although the advantage is quantitatively smaller. This confirms that the superiority holds, albeit with reduced margin, supporting the robustness claim. revision: yes

Referee: §3 (SNR and QCB derivations): The explicit expressions for the output quadratures or moments used to compute SNR (and the Gaussian-state QCB formula) are performed only under the distinct-temperature, independent-BS choice; the manuscript should add a brief check or note on how the SNR gap behaves if shared phase or loss correlations are introduced.

Authors: We have incorporated a brief note in the revised Section 3 addressing this point. The model assumes independent beam splitters because the sequential interactions occur at different times and locations, making shared correlations unlikely in the standard setup. If phase or loss correlations were present, the covariance matrix would include additional cross terms, potentially affecting the SNR. However, for the independent case considered, the derivations and the observed SNR gap remain valid. A full exploration of correlated noise models is beyond the current scope but noted as a direction for future work. revision: partial

Referee: QCB comparison paragraph: The claim of a 'sufficiently lower QCB than in previously reported results' requires explicit citation of the specific prior works and quantitative benchmarks (numerical values or a table) to allow assessment of the improvement in distinguishability.

Authors: We thank the referee for highlighting this issue. We have revised the relevant paragraph to include explicit citations to the prior works on QCB in quantum illumination (specifically, references to the studies using Gaussian states and Chernoff bounds for target detection). Additionally, we have added a table comparing the QCB values obtained in our sequential model with those from previous reports, providing numerical benchmarks that demonstrate the improvement in the low-reflectivity limit under thermal noise. revision: yes