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Effect of squeezing operations in two-mode Gaussian quantum illumination

MuSeong Kim, Mi-Ra Hwang, Eylee Jung, DaeKil Park

Published Nov 17, 2021• 0 citations
OpenAlex

Abstract

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 $r_1$ and $r_2$ respectively. The final quantum Bhattacharyya (QB) bound between $\rho_0$ (state for target absence) and $\rho_1$ (state for target presence) is shown to be independent of $r_2$. Compared to the classical coherent quantum illumination, we achieve the quantum advantage by $(6 + 10 \log_{10} (2 n_1 + 1))$ dB, where $n_1 = \sinh^2 r_1$. Second, we examine the effect of the two-mode squeezing operation, whose squeezing parameter is $r$. If $r \neq 0$, the dominant term of the exponential factor in the resulting QB bound is independent of $N_S$, where $N_S$ is the average photon number per signal mode. Since $N_S \ll 1$ is assumed, the tremendously huge quantum advantage can be achieved by controlling $r$.

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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.
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.
Quantum illumination is to discern the presence or absence of a target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small, the exponential decay constant can be computed using monotone metrics. We explicitly derive analytic formula for the decay constant of an arbitrary Gaussian input state in terms of first- and second-order moments assuming a low reflectivity target. Especially, further assuming large background noise, there is no need of symplectic diagonalization, which highly complicates the computation of decay constants. First, we show that the performance of a displaced two-mode squeezed vacuum (TMSV) state with low squeezing can be similar to that of a TMSV state with high squeezing. Second, we show that it is of utmost importance to prepare an efficient idler memory to outperform coherent states while providing a criterion on the idler memory transmittivity. Finally, we identify the region of physically possible correlations between the signal and idler modes that can outperform coherent states.
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.
We propose Gaussian quantum illumination(QI) protocol exploiting asymmetrically squeezed two-mode(ASTM) state that is generated by applying single-mode squeezing operations on each mode of an initial two-mode squeezed vacuum(TMSV) state, in order to overcome the limited brightness of a TMSV state. We show that the performance of the optimal receiver is enhanced by local squeezing operation on a signal mode whereas the performance of a realistic receiver can be enhanced by local squeezing operations on both input modes. Under a fixed mean photon number of the signal mode, the ASTM state can be close to the TMSV state in the performance of QI while there is a threshold of beating classical illumination in the mean photon number of the initial TMSV state. We also verify that quantum discord cannot be a resource of quantum advantage in the Gaussian QI using the ASTM state, which is a counterexample of a previous claim.
Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as, e.g., multimode entangled states. Our proof is based on a fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.