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arXiv:2406.10533

Long-Range Entangled Quantum Noise Radar Over Order of Kilometer

Hossein Allahverdi, Ali Motazedifard

Published Feb 22, 2024• 1 citation
arXivHTMLPDF

Abstract

In this paper, an explicit expression for the maximum detection range of an entangled quantum two-mode squeezed (QTMS) radar, in which a two-mode squeezed vacuum state of microwave electromagnetic fields is used, have been derived by considering both the quantum properties of the entangled microwave fields and radar parameters. By comparing this equation with that of traditional radars, we showed that one can though a QTMS radar as a traditional radar with a reduced threshold signal-to-noise ratio. By discussing the current limitations, it has been shown that the critical parameter to have both simultaneous quantum advantage and substantial radar range is increasing the bandwidth of the generated output signal in the quantum entangled source. It has been shown that by considering the current feasible system parameters, it is possible to implement a QTMS radar with maximum detection range up to the order of $2\mathrm{km}$, which is suitable for recognizing small unmanned aerial vehicles in urban distances. Moreover, based on the false alarm rate, we introduce two classes of early alarm and track QTMS radars. The present approach can be generalized to other quantum radars with different types of quantum sources like electro-opto-mechanical sources, and also may shed new light on investigating the quantum radar system toward practical applications. Finally, we have discussed the potential outlooks to improve and develop the quantum entangled radar systems to be practical from the engineering point of view.

DOI
10.36227/techrxiv.170862126.64515052/v1

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Quantum radars use phenomena from quantum physics, such as quantum entanglement, to enhance detection performance compared with classical radars.This thesis presents an end-to-end analysis of an entanglement-based radar called quantum two-mode squeezing radar (QTMS radar).This type of radar is of particular interest because a QTMS radar experiment has actually been performed, and because QTMS radars are closely related to a type of classical radar known as noise radar (NR).As part of the analysis, we develop a mathematical theory of QTMS radars and show that QTMS radars and NRs can be united under a single probabilistic model.We then show how their signals are to be processed to determine the presence or absence of a target, and undertake an extensive analysis of the target detection performance of QTMS radars and NRs.These theoretical results are verified using data drawn from a QTMS radar experiment and a laboratory NR.One important conclusion, supported by both theory and experiment, is that the receiver operating characteristic curve for a QTMS radar is better than that of an NR with the same signal powers.Throughout the thesis, we emphasize the need to establish common ground between quantum physics and radar engineering, and it is hoped that the unified theory of QTMS radar and NR presented here will play a role in this. 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•Jan 1, 2023•3 citations
In this paper, an explicit expression for the maximum detection range of an entangled quantum two-mode squeezed (QTMS) radar, in which a two-mode squeezed vacuum state of microwave electromagnetic fields is used, have been derived by considering both the quantum properties of the entangled microwave fields and radar parameters. By comparing this equation with that of traditional radars, we showed that one can though a QTMS radar as a traditional radar with a reduced threshold signal-to-noise ratio. By discussing the current limitations, it has been shown that the critical parameter to have both simultaneous quantum advantage and substantial radar range is increasing the bandwidth of the generated output signal in the quantum entangled source. It has been shown that by considering the current feasible system parameters, it is possible to implement a QTMS radar with maximum detection range up to the order of 2km2\mathrm{km}2km, which is suitable for recognizing small unmanned aerial vehicles in urban distances. Moreover, based on the false alarm rate, we introduce two classes of early alarm and track QTMS radars. The present approach can be generalized to other quantum radars with different types of quantum sources like electro-opto-mechanical sources, and also may shed new light on investigating the quantum radar system toward practical applications. Finally, we have discussed the potential outlooks to improve and develop the quantum entangled radar systems to be practical from the engineering point of view.
This article presents a comprehensive analysis of two classes of quantum radars, including quantum direct-detection and quantum-entangled noise radars. In the first case, inspired by the well-established concept of single-photon LiDARs, we investigated the performance of single-photon radars, in which state-of-the-art single microwave-photon detectors are employed to enhance the detection sensitivity and enable the detection of weaker signals. We derived analytical expressions for the maximum detection range of both classes of quantum radars in terms of the Lambert W function, by considering all relevant system, target, and environmental parameters. Our formulation facilitates direct comparison of noise radars with direct-detection radars and suggests that a quantum-entangled noise radar can be regarded as an enhanced direct-detection radar with an effective threshold signal-to-noise ratio. Furthermore, we applied this framework to classical-correlated noise radars and defined the parameter range enhancement factor (REF) to quantify the superiority of quantum-entangled noise radars over their classical counterparts. Moreover, we introduced a rule-of-thumb for approximating the REF. We also examined the influence of limitations imposed by various microwave detection technologies. Our analysis shows that the conventional antennas limit the potential benefits of quantum-entangled noise radar systems. We also demonstrated that the optimal detection method for these radars is a microwave detector based on a quantum transducer combined with a single optical-photon detector. We showed that, with the current technology, implementing a quantum-entangled noise radar with the maximum detection range on the order of few kilometers is possible. Finally, we explored the potential applications of quantum-entangled noise radars.
Recently, the authors have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. This radar, which they call a quantum two‐mode squeezing radar (QTMS radar), generates a pair of entangled microwave signals and transmits one of them through free space, using the other signal as a reference to perform matched filtering. The specific type of entanglement is called a two‐mode squeezed vacuum, a type of continuous‐variable entanglement between two frequencies. Motivated by the success of these experiments, they try to better understand the entangled QTMS radar signals in this study. They do so by comparing it to a simpler, more conventional radar system, which they call a two‐mode noise radar (TMN radar). They also show how both types of radars are related to standard noise radars as described in the literature. They find that the signals for QTMS radar signals and TMN radar signals have the same mathematical form and that they are related to noise radar by a simple mathematical transformation. This shows that QTMS radar signals can be emulated by a fictional, idealised TMN radar and that it is possible to apply results from the noise radar literature to QTMS radar.
Many quantum radars currently studied in the literature use a phenomenon called entanglement to address the problem of distinguishing signal from noise, which is one of the most important problems faced by any radar. Until recently, entanglement-based quantum radars at radio frequencies existed only in theory; their practicality was very much in doubt. The situation has changed with a recent experimental implementation of all the necessary components of a quantum two-mode squeezing (QTMS) radar, which operates at microwave frequencies and can be described as a quantum range finder. In this article, we lay out the exact problem solved by this prototype, namely quantum noise, and explain how entanglement can overcome the existence of this noise. By analyzing the QTMS radar prototype, we point out a technological route to an entanglement-based quantum radar that can, in principle, perform all tasks that radars can and must do, such as array processing, clutter suppression, and image processing (including synthetic aperture radar and inverse synthetic aperture radar).
We have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. Because the signal generation process relies on quantum mechanical principles, the system is considered to contain a quantum-enhanced radar transmitter. This transmitter generates a pair of entangled microwave signals and transmits one of them through free space, where the one-way signal is measured using a simple and rudimentary receiver. The type of entanglement used is called two-mode squeezed vacuum (TMSV), so we may call our radar a quantum two-mode squeezing radar (QTMS radar). At the heart of the transmitter is a device called a Josephson parametric amplifier (JPA), which generates the entangled microwave beams; these are then sent through a chain of amplifiers. One beam passes through 0.5 m of free space; the other is measured directly. The two measurement results are correlated in order to distinguish noise from signal. We compare this quantum-enhanced transmitter to a similar one using only conventional components, and find that there is a significant gain when the two systems broadcast signals at approximately the same power.
We built and evaluated a prototype quantum radar, which we call a quantum two-mode squeezing (QTMS) radar, in the laboratory. It operates solely at microwave frequencies; there is no downconversion from optical frequencies. Because the signal generation process relies on quantum mechanical principles, the system is considered to contain a quantum-enhanced radar transmitter. This transmitter generates a pair of entangled microwave signals and transmits one of them through free space, where the signal is measured using a simple and rudimentary receiver. At the heart of the transmitter is a device called a Josephson parametric amplifier, which generates a pair of entangled signals called two-mode squeezed vacuums at 6.1445 and 7.5376 GHz. These are then sent through a chain of amplifiers. The 7.5376 GHz beam passes through 0.5 m of free space; the 6.1445 GHz signal is measured directly after amplification. The two measurement results are correlated in order to distinguish signal from noise. We compare our QTMS radar to a classical radar setup using conventional components, which we call a two-mode noise (TMN) radar, and find that there is significant gain when both systems broadcast signals at -82 dBm. This is shown via a comparison of receiver operating characteristic curves. In particular, we find that the quantum radar requires eight times fewer integrated samples compared to the TMN radar to achieve the same performance.
Quantum radars use phenomena from quantum physics, such as quantum entanglement, to enhance detection performance compared with classical radars.This thesis presents an end-to-end analysis of an entanglement-based radar called quantum two-mode squeezing radar (QTMS radar).This type of radar is of particular interest because a QTMS radar experiment has actually been performed, and because QTMS radars are closely related to a type of classical radar known as noise radar (NR).As part of the analysis, we develop a mathematical theory of QTMS radars and show that QTMS radars and NRs can be united under a single probabilistic model.We then show how their signals are to be processed to determine the presence or absence of a target, and undertake an extensive analysis of the target detection performance of QTMS radars and NRs.These theoretical results are verified using data drawn from a QTMS radar experiment and a laboratory NR.One important conclusion, supported by both theory and experiment, is that the receiver operating characteristic curve for a QTMS radar is better than that of an NR with the same signal powers.Throughout the thesis, we emphasize the need to establish common ground between quantum physics and radar engineering, and it is hoped that the unified theory of QTMS radar and NR presented here will play a role in this. List of TablesCommon sense imagines that when it sees a table it sees a table.This is a gross delusion.Bertrand Russell The ABC of Relativity 2.1 A taxonomy of quantum sensors 11 5.1 System parameters for Wilson's QTMS radar experiment 104 6.1 QTMS radar variables and parameters 127 6.2 Rice distribution parameters fitted to simulated values of ρ ˆ145 6.3 Parameter estimates for Wilson et al.'s QTMS radar prototype 151 6.4 TVD between theoretical and experimental PDFs for the QTMS radar 152 6.5 Transmit powers and parameter values for the experimental NR 153 6.6 TVD between theoretical and experimental PDFs for the NR 156 7.1 Parameter values for the ROC curve plots 196 8.1 Correlation coefficient vs. transmit power: fit parameters 210 8.2 Correlation coefficient vs. range: fit parameters 218 8.3 Noise radar system parameters used in Example 8.10 232 8.4 QTMS radar system parameters used in Example 8.11 233 B.1 Relationships between probability distributions 281 xvi List of Figures As the Chinese say, 1001 words is worth more than a picture.John McCarthy 3.1 Time evolution of coherent states 64 3.2 Vacuum noise in a beam splitter 68 4.1 Target detection using a detector and a threshold 77 4.2 Probabilities of detection and false alarm for the envelope detector 78 4.3 ROC curves for the envelope detector 83 4.4 ROC curves for the NP detector (sinusoidal radar) compared with those for the envelope detector 92 5.1 Illustration of the basic QI protocol 95 5.2 Block diagram of Wilson's QTMS radar setup 102 5.3 Horn antennas used in the Wilson experiment 102 5.4 Interior and exterior of the dilution refrigerator 105 5.5 Interior of the can containing the JPA 106 5.6 Simplified diagram of a JPA 108 5.7 JPA mounted on a printed circuit board 109 5.8 Block diagram of the benchmark NR for the Wilson experiment 110 6.1 Correlation number line 135 6.2 Separable, entangled, and forbidden values of ρ as a function of σ 1 135 6.3 PDF of σ ˆ1 141 xvii LIST OF FIGURES xviii 6.4 Exact and approximate PDFs of ρ ˆ143 6.5 TVD between the exact and approximate PDFs of ρ ˆ146 6.6 Concentration parameter vs. Nρ 2 148 6.7 Exact and approximate PDFs of φ ˆ149 6.8 TVD between the exact and approximate PDFs of φ ˆ149 6.9 Theoretical and experimental PDFs for the QTMS radar 151 6.10 Theoretical and experimental PDFs for the experimental NR with transmit power -18.91 dBm 154 6.11 Theoretical and experimental PDFs for the experimental NR with transmit power -9.380 dBm 154 6.12 Theoretical and experimental PDFs for the experimental NR with transmit power 1.955 dBm 155 7.1 PDF of the NP detector (target present) 169 7.2 PDF of the NP detector (target absent) 170 7.3 LIST OF FIGURES xix 8.3 Correlation coefficient vs. range 8.4 ROC curves for the MF detector for various ranges 8.5 Correlation coefficient vs. range for an experimental NR 8.6 ROC curves for all detectors when ρ → 0 and N → ∞ 8.7 ROC curve for the MF detector when ρ → 0 and N → ∞: increasing ρ vs. increasing N 8.8 Probability of detection vs. Nρ 2 when ρ → 0 and N → ∞ 8.9 ROC curves for D MF and ρ ˆwhen ρ is large and N is small 8.10 ROC curves for the Wilson experiment, showing the increase in N required for the benchmark NR to match the QTMS radar 8.11 Maximum range vs. ρ 0 and N when p d = 0.9 and p fa = 10 -6 D.1 Simplified block diagram of the NR setup D.2 Photograph of the NR setup D.3 NR aimed at a wall D.4 Corner reflector used for the experiment in Section 8.2to x 0 in a given situation, without asserting that x = x 0 elsewhere.An index of symbols and abbreviations used in this thesis, together with the page at which each symbol or abbreviation is first defined, is included at page 262.The reader is encouraged to make liberal use of this index.