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arXiv:2302.07498 · Physical Review Research

Gaussian quantum illumination via monotone metrics

Dong Hwan Kim, Yonggi Jo, Duk Y. Kim, Taek Jeong, Ji‐Hwan Kim, Nam Hun Park, Zaeill Kim, Su‐Yong Lee

Published Jul 6, 2023• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.5.033010

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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.
It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach with all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detection on both modes.
We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical regime using a thermal state, a receiver implemented with a photon number difference measurement approaches its bound regardless of the signal mean photon number, while it asymptotically approaches the classical bound in the limit of a huge idler mean photon number.
In quantum illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. For bright thermal backgrounds, we show that the QI system using multiple copies of low-brightness two-mode squeezed vacuum states is nearly optimal. More generally, our results place limits on the best possible performance achievable using QI systems at all wavelengths, and at all signal and background noise levels.
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 optimal observables for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The optimal observables dominantly consist of off-diagonal components of output states, which is implemented with feasible setups. In the quantum regime using a two-mode squeezed vacuum state, the receiver implemented with heterodyne detections outperforms the other feasible receivers, which asymptotically improves the error probability exponent by a factor of two over the classical state bound. In the classical regime using coherent or thermal states, the receiver implemented with photon number difference measurement asymptotically approaches its bound.
Abstract In analyses of target detection with Gaussian state transmitters in a thermal background, the thermal occupation is taken to depend on the target reflectivity in a way which simplifies the analysis of the symmetric quantum hypothesis testing problem. However, this assumption precludes comparison of target detection performance between an arbitrary transmitter and a vacuum state transmitter, i.e. ‘detection without illumination’, which is relevant in a bright thermal background because a target can be detected by its optical shadow or some other perturbation of the background. Using a target-agnostic thermal environment leads to the result that the oft-claimed 6 dB possible reduction in the quantum Chernoff exponent for a two-mode squeezed vacuum transmitter over a coherent state transmitter in high-occupation thermal background is an unachievable limiting value, only occurring in a limit in which the target detection problem is ill-posed. Further analyzing quantum illumination in a target-agnostic thermal environment shows that a weak single-mode squeezed transmitter performs worse than ‘no illumination’, which is explained by the noise-increasing property of reflected low-intensity squeezed light.