Channel superposition mitigates photon loss errors in quantum illumination

In quantum illumination, the probe and idler photons are entangled, and both are jointly measured at the end. The entanglement between the probe and idler photons enhances the detection performance per unit average photon number in the probe mode, particularly in low-reflectivity and high-noise scenarios. However, photon loss degrades the absolute detection performance and progressively reduces the performance gain relative to optimal classical strategies by diminishing non-classical correlations. To address this, we employ a channel superposition framework that encompasses two types of channel superposition protocols: indefinite causal order (ICO) and path superposition with a disjoint environment (PS-DE). Under the effective erasure/fading loss model adopted for the low-brightness regime, our analytical and numerical analysis based on the quantum Chernoff bound shows that both ICO and PS-DE can, in principle, achieve an advantage. The advantage persists as long as non-zero interference remains, reverting to the performance of standard quantum illumination once the interference is completely suppressed. Crucially, within this model, the ICO protocol is significantly more robust, maintaining a tighter upper bound on the error probability than standard quantum illumination and the PS-DE approach. This performance hierarchy is rooted in their fundamental structures: ICO exploits a shared environment to generate stronger quantum interference, while PS-DE, relying on disjoint environments, offers a more experimentally tractable, albeit weaker, alternative.