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arXiv:2107.05203 · Quantum Information Processing

Quantum illumination with three-mode Gaussian state

Eylee Jung, DaeKil Park

Published Jan 28, 2022• 8 citations
arXivHTMLPDF

Abstract

Abstract The quantum illumination is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that the quantum Bhattacharyya bound between $$\rho $$ ρ (state for target absence) and $$\sigma $$ σ (state for target presence) is less than the previous result derived by two-mode Gaussian state when $$N_S$$ N S , average photon number per signal, is less than 0.295. This indicates that the quantum illumination with three-mode Gaussian state gives less error probability compared to that with two-mode Gaussian state when $$N_S < 0.295$$ N S < 0.295 .

DOI
10.1007/s11128-021-03359-8

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Abstract The quantum illumination is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that the quantum Bhattacharyya bound between ρ\rho ρ ρ (state for target absence) and σ\sigma σ σ (state for target presence) is less than the previous result derived by two-mode Gaussian state when NSN_SNS​ N S , average photon number per signal, is less than 0.295. This indicates that the quantum illumination with three-mode Gaussian state gives less error probability compared to that with two-mode Gaussian state when NS<0.295N_S < 0.295NS​<0.295 N S < 0.295 .
Quantum illumination with asymmetric strategy is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that this scenario gives less-error probability compared to that with the two-mode squeezed vacuum state when NSN_SNS​, average photon number per signal, is less than 0.460.460.46.
Effect of the squeezing operations is examined in two-mode Gaussian quantum illumination. First, we consider two single-mode squeezing operation, whose squeezing parameters are r1r_1r1​ and r2r_2r2​ respectively. The final quantum Bhattacharyya (QB) bound between ρ0\rho_0ρ0​ (state for target absence) and ρ1\rho_1ρ1​ (state for target presence) is shown to be independent of r2r_2r2​. Compared to the classical coherent quantum illumination, we achieve the quantum advantage by (6+10log⁡10(2n1+1))(6 + 10 \log_{10} (2 n_1 + 1))(6+10log10​(2n1​+1)) dB, where n1=sinh⁡2r1n_1 = \sinh^2 r_1n1​=sinh2r1​. Second, we examine the effect of the two-mode squeezing operation, whose squeezing parameter is rrr. If r≠0r \neq 0r=0, the dominant term of the exponential factor in the resulting QB bound is independent of NSN_SNS​, where NSN_SNS​ is the average photon number per signal mode. Since NS≪1N_S \ll 1NS​≪1 is assumed, the tremendously huge quantum advantage can be achieved by controlling rrr.
It is shown that quantum illumination with three photons non-Gaussian states, where the signal is described by a two photons state and the idler is described by a one photon state, can outperform in sensitivity standard Gaussian quantum illumination in a high noisy background. In particular, there is a reduction in the probability due to an increase in the probability of error exponent by a factor 1/NS1/{N_S}1/NS​, where NSN_SNS​ is the average number of photons per mode of the signal state.
Quantum illumination is a quantum sensing protocol primarily used for object detection, which aims to detect the presence of a target with low reflectivity in the free space using quantum light fields. Here we investigate a quantum illumination scheme using an entangled light source by performing non-Gaussian operations on the two-mode squeezed vacuum (TMSV) state in order to reduce the detection error probability and meanwhile improve the signal-to-noise (SNR) ratio. We demonstrate that under the same squeezing parameter, the non-Gaussian operations can significantly reduce the detection error rate compared with the original TMSV state. Under the same average signal photon number, both the TMSV states with and without non-Gaussian operations can provide smaller error rate than that of the coherent state. In addition, we consider the balanced homodyne detection on idler and return signal photons as joint measurement and find that non-Gaussian operations can enhance the SNR of target detection by about 6--9 dB compared with that using TMSV. These results here demonstrate the advantage of the non-Gaussian entangled source in quantum illumination protocol and can find potential applications in target detection in noisy environment.
An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.
Quantum illumination makes use of the strong correlation between entangled photons, making it possible to detect targets that break through physical limits. The Gaussian entangled state is a continuous variable entangled state with a high number of Hilbert spatial modes, which is currently a viable alternative to quantum lighting. In order to explore the target detection ability of Gaussian entangled state, this paper starts from the Gaussian entanglement model of Lloyd, establishes the target detection error probability boundary model under Gaussian entangled quantum illumination, and explores the optimal detection condition of Gaussian entangled state based on the detection signal-to-noise ratio and the number of measurements. The results show that when the Gaussian entangled state is optimal for the coherent state, the number of measurements is inversely proportional to the signal-to-noise ratio. Under the same error probability, the difference between the detection distances of the two states is determined by the atmospheric attenuation coefficient. The smaller the attenuation coefficient is, the smaller the attenuation coefficient is, the difference is greater.