Quantum Illumination with a Hetero-Homodyne Receiver and Sequential Detection

We propose a hetero-homodyne receiver for quantum illumination (QI) target detection. Unlike prior QI receivers, it uses a cascaded positive operator-valued measurement (POVM) that does not require a quantum interaction between QI’s returned radiation and its stored idler. When used without sequential detection its performance matches the 3-dB quantum advantage over optimum classical illumination (CI) that Guha and Erkmen’s [Phys. Rev. A 80, 052310 (2009)] phase-conjugate and parametric amplifier receivers enjoy. When used in a sequential detection QI protocol, the hetero-homodyne receiver offers a 9-dB quantum advantage over a conventional CI radar, and a 3-dB advantage over a CI radar with sequential detection. Our work is a significant step forward toward a practical quantum radar for the microwave region, and, more generally, emphasizes the potential offered by cascaded POVMs for quantum radar.

Figure 1

Sketch of Tan et al.’s QI protocol with hetero-homodyne reception. A signal-idler system is initialized in an $M$ mode-pair TMSV state, with each signal and idler mode containing $N_S\ll 1$ photons on average. The signal is sent to test for the presence of a weakly reflecting (roundtrip transmissivity $\kappa \ll 1$) target embedded in high-brightness background noise ($N_B\gg 1$ photons/s-Hz). The hetero-homodyne receiver measures the cross-correlation between the returned radiation and the idler. Because the low-brightness TMSV mode pairs’ phase-sensitive cross-correlation $\sqrt{N_S(N_S+1)}$ greatly exceeds the classical limit $N_S$, QI outperforms classical illumination in this regime even though loss and noise have destroyed the TMSV states’ initial entanglement. het, heterodyne; hom, homodyne; FF, feedforward.

Figure 2

Schematic of the hetero-homodyne receiver. Thick arrows represent quantum microwave fields. Thin arrows represent baseband signals that are conditioned on the outcome of the heterodyne measurement.

Figure 3

Simulated probability distributions for the number of SPRT trials used by CI and QI assuming $N_S=0.01$, $\kappa =0.01$, $N_B=100$, $M_S={10}^5$, and $\alpha =\beta ={10}^{-4}$. Each distribution is generated from ${10}^6$ simulated experiments for each hypothesis.

Figure 4

CI and QI error probabilities versus average number of transmitted signal photons, $N_T$, assuming $N_S=0.01$, $\kappa =0.01$, and $N_B=100$. The solid curves are theory results from Eqs. (9) and (27) for nonsequential CI with homodyne detection and nonsequential QI with hetero-homodyne detection, respectively. The points are simulated error probabilities for sequential CI with homodyne detection and sequential QI with hetero-homodyne detection with $M_S={10}^5$ for $\alpha =\beta ={10}^{-1},{10}^{-2},{10}^{-3},{10}^{-4}$, and ${10}^{-5}$. Each point is generated from ${10}^6$ simulated experiments for each hypothesis. See the text for how the dashed curves are obtained.

Figure 5

Schematic of a hetero-homodyne receiver without quantum memory. Thick arrows represent quantum microwave fields. Thin arrows represent baseband signals that are conditioned on the outcome of the heterodyne measurement.