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

Quantum illumination is a protocol for detecting a low-reflectivity target by using two-mode entangled states composed of signal and idler modes, which can outperform unentangled states. We study multi-qudit states for single-shot detection limits of quantum illumination under white noise environment. Using three-qubit states, we obtain that the performance is enhanced by the entanglement between signal and idler qubits, whereas it is degraded by the entanglement between signal qubits. The similar behaviors are also observed for three-qutrit, four-qubit, and four-ququart states. In particular, the optimal state is not a maximally entangled multipartite state but a combination of a maximally entangled bipartite state. Moreover, we show that quantum correlation can explain the quantum advantage of three-qubit, three-qutrit, and four-qubit states, with exception of a four-ququart state.

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