In this paper, we provide a simple introduction to the enhancement achievable by quantum radars. We show that an important type of quantum radar, known as quantum two-mode squeezing (QTMS) radar, is mathematically connected to noise radars. The quantum advantage stems from QTMS radar’s ability to mitigate the effect of quantum noise, leading to greater contrast in the matched filter output between the target present and target absent cases. This reduced the integration time needed to detect a target. For imaging applications that rely on matched filtering, the quantum enhancement leads to a speedup in imaging as well.
In this paper, we provide a simple introduction to the enhancement achievable by quantum radars. We show that an important type of quantum radar, known as quantum two-mode squeezing (QTMS) radar, is mathematically connected to noise radars. The quantum advantage stems from QTMS radar’s ability to mitigate the effect of quantum noise, leading to greater contrast in the matched filter output between the target present and target absent cases. This reduced the integration time needed to detect a target. For imaging applications that rely on matched filtering, the quantum enhancement leads to a speedup in imaging as well.
Quantum two-mode squeezing (QTMS) radars and noise radars perform matched filtering of the received signal using a reference signal stored within the radar. Their target detection performance depends on the correlation between the received and reference signals, and the improved detection performance of QTMS radars over noise radars is due to the fact that it has an increased correlation. In this paper, we present a novel way of understanding how detection performance depends on the correlation by relating the correlation to the integration time. Concretely, we prove that increasing the correlation by a given factor is equivalent to increasing the integration time by the square of that factor. We apply this result to a recent QTMS radar experiment where the increase in correlation was approximately a factor of 3. This was found to be equivalent to increasing the integration time by a factor of 9, thus confirming the validity of our result and approximation.
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.
Recent experimental results have demonstrated gains in sensing capability using novel possibilities offered by quantum mechanics. In particular, a prototype radar which uses quantum techniques to enhance detection ability has been built in a laboratory, showing that quantum radars at RF frequencies are feasible. This prototype is called a quantum two-mode squeezing radar (QTMS radar). In this paper, we use the QTMS radar as a springboard to review the concept of quantum squeezing. We find that Josephson parametric amplifiers (JPAs), one of which was used in the QTMS radar prototype, can be employed to produce two-mode and one-mode squeezed states at RF frequencies. We then briefly discuss some of the possible applications of such states to the field of radar engineering.
Quantum two-mode squeezing (QTMS) radars and noise radars detect targets by correlating the received signal with an internally stored recording. A covariance matrix can be calculated between the two which, in theory, is a function of a single correlation coefficient. This coefficient can be used to decide whether a target is present or absent. We can estimate the correlation coefficient by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Using simulated data, we show that the estimates follow a Rice distribution whose parameters are simple functions of the underlying, “true” correlation coefficient as well as the number of integrated samples. We obtain an explicit expression for the receiver operating characteristic curve that results when the correlation coefficient is used for target detection. This is an important first step toward performance prediction for QTMS radars.
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.
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).