Single-shot detection limits of quantum illumination with multi-qudit states

We study multi-qudit states for single-shot detection limits of quantum illumination under white noise environment. We show that the optimal state is not a maximally entangled multipartite state but a combination of a maximally entangled bipartite state, since entanglement between signal states degrades the performance. The behaviors are obtained in the cases of three-qubit, three-qutrit, four-qubit, and four-ququart states, where the multi-qudit states can outperform the two-qubit entangled states. Moreover, we find that quantum correlation of the multi-qudit states can explain the quantum advantage over the two-qubit entangled states, but it is not valid for four-ququart states.