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arXiv:2309.04086

Asymmetric Quantum Illumination with three-mode Gaussian State

Mi-Ra Hwang, DaeKil Park

Published Sep 8, 2023• 0 citations
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Abstract

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 $N_S$, average photon number per signal, is less than $0.46$.

DOI
10.48550/arxiv.2309.04086

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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.
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 .
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.
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.
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 takes advantage of quantum entanglement to achieve low error probability for detecting a low reflective object embedded in a noisy thermal bath. The two-mode squeezed state (TMSS), which is a Gaussian state, has been applied to quantum illumination as the detecting states in experiment. The photon-subtracted TMSS has also been proposed to achieve even lower error probability. Here we study quantum illumination with non-Gaussian states generated by photon subtraction and photon addition. Helstrom limit and quantum Chernoff bound are evaluated for comparison between performance of states with the same squeezing strength and with the same signal strength, respectively. Particularly, states generated by asymmetrical coherent superposition of photon subtraction and addition are studied, which are shown by us to have better performance than symmetrical ones. We show that non-Gaussian operations enhance the quantum illumination by introducing both stronger entanglement and signal strength. We then give a strategy on how to choose the optimal states for the best performance in different scenarios.