It has been discussed recently how quantum illumination can be used to increase the accuracy of the value range-delay measurement \cite{Zhuang Shapiro 2022} in the domain of SNR compatible with current radar systems. However, the advantage described in [1] requires of a large integration time. In this work it is argued that multiple entangled photon quantum illumination could help to reduce the integration time when evaluating range-delay. Our analysis is performed in the framework of three entangled photon states discrete quantum illumination protocols. In this setting it is shown explicitly that using a direct generalization of Lloyd's protocol to the case where signal states describe two photons presents interesting advantages: 1. The reduction of the probability of error with respect to Lloyd's quantum illumination, 2. The reduction of the integration time with respect to Lloyd's quantum illumination, 3. The increase in the ultimate in the measurement of the range-delay accuracy.
It has been discussed recently how quantum illumination can be used to increase the accuracy of the value range-delay measurement \cite{Zhuang Shapiro 2022} in the domain of SNR compatible with current radar systems. However, the advantage described in [1] requires of a large integration time. In this work it is argued that multiple entangled photon quantum illumination could help to reduce the integration time when evaluating range-delay. Our analysis is performed in the framework of three entangled photon states discrete quantum illumination protocols. In this setting it is shown explicitly that using a direct generalization of Lloyd's protocol to the case where signal states describe two photons presents interesting advantages: 1. The reduction of the probability of error with respect to Lloyd's quantum illumination, 2. The reduction of the integration time with respect to Lloyd's quantum illumination, 3. The increase in the ultimate in the measurement of the range-delay accuracy.
Abstract In this work, a theoretical generalization of Lloyd's quantum illumination model for signal beams described by two entangled photon states is developed. It is shown that the new protocol is more sensitive than Lloyd's model with respect to signal‐to‐noise ratio (SNR) and reduces the required time‐bandwidth product to have the same enhancement in the SNR. The protocol is resilient against noise, potentially resilient against losses, and offers a method to find the range of the target. However, the generation of the required three photon states for the protocol remains a technical problem for its practical implementation.
Radars use time-of-flight measurement to infer the range to a distant target from its return's round-trip range delay. They typically transmit a high time-bandwidth product waveform and use pulse-compression reception to simultaneously achieve satisfactory range resolution and range accuracy under a peak transmitted-power constraint. Despite the many proposals for quantum radar, none have delineated the ultimate quantum limit on ranging accuracy. We derive that limit through continuous-time quantum analysis and show that quantum illumination ranging-a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and and a high time-bandwidth product retained idler pulse-achieves that limit. We also show that quantum illumination ranging offers mean-squared range-delay accuracy that can be tens of dB better than that of a classical pulse-compression radar of the same pulse bandwidth and transmitted energy.
Quantum illumination is one of the most basic ways to realize the quantum radar for detection of low-reflectivity targets embedded in a thermal-noise bath. It preserves a strong advantage over the classical counterparts even though its fragile quantum entanglement is completely destroyed by a large amount of noise and losses. In this paper, we describe and analyze a discrete-variable quantum illumination system with ancillary degrees of freedom of entangled photon pairs. Comparing the error probability bound, i.e., the quantum Chernoff bound, we identify that this system indeed offers higher accuracy than the single-photon illumination and quantum illumination with single degree of freedom of entangled photon pairs. Furthermore, the utilization of ancillary degrees of freedom exponentially enhances signal-to-noise ratio over quantum illumination without ancillary degrees of freedom. It means that this system reduces the necessary amount of signal photons to accurately determine whether the object is present or absent in the target region, which is absolutely crucial to the stealthiness of the radar system.
Quantum radar uses the strong correlations of entangled photons and has a great potential to improve the detection sensitivity. Recently, many research results have been achieved in theoretical analysis and experiments on the performance advantages of quantum illumination radar. However, there are limited researches on its detection range. Based on the analysis of the noise tolerance of entangled state photons, we study the advantages of quantum illumination radar in detection range based on radar equation. It is shown that the detection range of quantum illumination radar is larger than that of classical radar in some regimes due to the strong noise suppression ability of quantum radar.
Quantum illumination (QI) is an entanglement-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer a true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. A recent QI study by Armanpreet Pannu, Amr Helmy, and Hesham El Gamal (PHE), however, has: (i) combined the entangled state from Lloyd’s QI with the channel models from Gaussian-state QI; (ii) proposed a new positive operator-valued measurement for that composite setup; and (iii) claimed that, unlike Gaussian-state QI, PHE QI achieves the Nair–Gu lower bound on QI target-detection error probability at all noise brightnesses. PHE’s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. The current paper works out the finite-dimensional performance of PHE QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair–Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair–Gu bound, PHE QI requires enormously higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has an appreciable quantum advantage in low-brightness (much less than 1 photon/mode) noise.
Quantum illumination proposed by Lloyd is a protocol that detects the existence of a target by using entangled light of two-mode. Quantum illumination was first proposed using the Bell state, and then the use of a two-mode Gaussian state was proposed. On the other hand, there are many impact studies using the quasi-Bell state. However, as far as we know, there are no studies that analyze quantum illumination using the quasi-Bell state. Therefore, we focused on the performance evaluation of quantum illumination using the quasi-Bell state in this paper. We compared and considered the effects using the Bell state, the two-mode Gaussian state, the maximum quasi-Bell state, the non-maximum quasi-Bell state, and the coherent state (i.e., a laser radar) on the attenuated channel. In particular, we derived the exact solutions of the error probabilities when using the maximum and non-maximum quasi-Bell states. Then we clarified that quantum illumination using the quasi-Bell state offers a clear advantage over that using the other entangled states under almost situations and always offers a clear advantage over the laser radar.