Performance analysis for high-dimensional Bell-state quantum illumination (2409.08574v2)

Abstract: Quantum illumination (QI) is an entanglement-based protocol for improving lidar/radar detection of unresolved targets beyond what a classical lidar/radar of the same average transmitted energy can do. Originally proposed by Lloyd as a discrete-variable quantum lidar, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. Recently, however, Pannu et al. (arXiv:2407.08005 [quant-ph]) have: (1) combined the entangled state from Lloyd's QI with the channel models from Gaussian-state QI; (2) proposed a new positive operator-valued measurement for that composite setup; and (3) claimed that, unlike Gaussian-state QI, their QI achieves the Nair-Gu lower bound on QI target-detection error probability at all noise brightnesses. Pannu et al.'s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. This paper works out the finite-dimensional performance of Pannu et al.'s QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair-Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair-Gu bound's, Pannu et al.'s QI requires much higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has appreciable quantum advantage in low-brightness (<<1 photon/mode) noise.