David Luong, Bhashyam Balaji, Sreeraman Rajan
©SHUTTERSTOCK.COM/LEKKYSTOCKPHOTO
Quantum radar is a fledgling new technology that promises gains in detection performance. However, there are challenges standing in the way of their implementation. In this article, three classes of quantum radars are discussed: quantum interferometric radar, quantum illumination radar, and quantum two-mode squeezing (QTMS) radar. Of these, the last-named is the closest to being implemented in real life, though it is by no means the last word on the subject. In conclusion, we find that quantum radars are at least worth studying further.
What is a quantum radar? As a matter of fact, any radar that exploits quantum mechanical phenomena to perform target detection can be called a quantum radar. Of course, at a fundamental level, all phenomena are quantum mechanical. When we speak of quantum radars, however, we usually mean radars that exploit distinctively quantum phenomena that are absent from conventional radars. This can potentially lead to improvements in many types of radar, including pulsed radar, continuous-wave radar, and noise radar. In this article, we will show that there are great challenges in the way of building such radars, but that these challenges are by no means insurmountable. It is worth making an attempt to surmount these obstacles because quantum radars have the potential to deliver improved performance in applications where conventional radars might fall short.
One of the great surprises of quantum radar is that quantum physics can, in fact, be exploited to enhance radar detection performance. This is not at all an obvious proposition, as quantum mechanical effects tend to become significant only at very short length scales, on the order of single atoms. (Obviously, the consequences of quantum mechanical effects are important at larger length scales, but for large systems, they average out and can be described using classical physics.) Radars themselves are far larger than atoms, and the targets they are used to detect are likewise much larger than atoms. Moreover, many quantum phenomena—such as entanglement—are fragile, as evidenced by the challenges to building a quantum computer, so one would expect them to be of limited utility to sensing, if at all. Yet, it has been shown that quantum effects can be used to improve radar detection. This is all the more surprising because the two pillars of modern physics, quantum mechanics and relativity, both seem equally inapplicable to radars. (Radars and their targets do not travel at speeds near the speed of light, nor are they heavy enough for gravity to become significant.) But relativistic radars have never been proposed, while quantum radar experiments have already been performed in the laboratory.
In 2008, Dowling proposed that a previously known technique called quantum interferometry could be applied to remote sensing [1]. Quantum interferometry is not known to increase the probability of detecting a given target, but it has the potential to increase range resolution beyond that which conventional radars are capable of. Coincidentally, it was also in 2008 that Lloyd proposed a completely different target sensing protocol called quantum illumination [2]. Unlike quantum interferometry, quantum illumination does not result in higher range sensitivity, but it does result in higher detection probabilities. These were the first indications that measurements done with quantum radar could be used to achieve better estimates. These indications were enough to inspire the world’s first book on quantum radar, written by Lanzagorta in 2011 [3], to which we refer the reader for a summary of the history of the field up to that point.
Both quantum interferometry and quantum illumination rely on one of the most famous quantum phenomena: entanglement. We will see, however, that they use very different types of entangled electromagnetic signals and exploit those signals in very different ways. It turns out that quantum illumination is far more practical in the short term. For this reason, the history of quantum radar up to the present moment is effectively synonymous with the history of quantum illumination, and we will focus on quantum illumination and closely related protocols in this section. Nevertheless, it may be too early to consign quantum interferometry to the dustbin of history just yet. In fact, it could potentially be very useful in some applications, especially biomedical applications. Nor can we discount the possibility of future quantum radars based on other quantum techniques.
The original quantum illumination article by Lloyd contained only a simplified analysis and somewhat overstated the potential gain in detection performance of a quantum illumination radar. It also relied on single-photon entangled states, which are very difficult to generate. Luckily, Tan et al. performed a fuller analysis soon after Lloyd’s article was published [4]. They showed that quantum illumination can be implemented using a type of entangled signal known as two-mode squeezed vacuum, which is much easier to generate than single-photon entanglement. Furthermore, their detailed analysis shows that, although Lloyd’s results were too optimistic, quantum illumination does lead to a gain over a monochromatic continuous-wave radar of the same transmit power. Unfortunately, this gain is stated in very abstract terms which were not meaningful to engineers. Tan et al. couched the gain in the following terms: “the quantum illumination system realizes a 6-dB advantage in the error-probability exponent.” (In later work, some authors would conflate this 6 dB with an “effective signal-to-noise ratio (SNR)”, but no author has ever proven explicitly that the error-probability exponent has anything to do with SNR as understood by engineers.)
Due to the fact that quantum illumination’s stated 6-dB advantage does not correspond to any of the established figures of merit in the radar and measurement community, there was much skepticism among radar engineers as to whether quantum illumination—or quantum radar as a whole—was worth exploring at all. For the next several years, almost all advances in quantum illumination came from physicists. (For an overview of these theoretical advances, see [5]. This magazine article was written by Shapiro, the leader of the research group of which Tan was a member.) It is true that quantum illumination lidars were demonstrated in the laboratory, but from an engineering perspective, there is a vast difference between visible light and microwaves.
This situation changed in 2019 when a research group led by Wilson performed the world’s first experiment that demonstrated all of the components of a quantum radar at microwave frequencies, from signal generation to free-space transmission to signal reception. The protocol implemented was a variation of quantum illumination which was called quantum-enhanced noise radar for a physics audience [6] and QTMS radar for an engineering audience [7]. (We note, however, that the experiment was not a true quantum radar because it included amplifiers which broke the entanglement. They would have to be removed in a true quantum radar setup.) This experiment was analyzed using receiver operating characteristic (ROC) curves, which is the gold standard for quantifying radar detection performance and which is far more congenial to radar engineers than the error-probability exponent. Among other results, it was found that a comparable classical radar at the same transmit power would need to increase its integration time by a factor of eight in order to achieve the same performance as a QTMS radar.
The QTMS radar experiment added new vigor to the field of quantum radar by demonstrating to radar engineers that quantum radars are experimentally feasible. Moreover, a subset of the results of the QTMS radar experiment were quickly confirmed by an independent quantum radar experiment performed by Barzanjeh et al. [8], which buttressed the conclusions of [6], [7]. This has led to a boom in quantum radar publications, many of them suggesting intriguing directions for future research [9], [10], [11] , [12], [13], [14], [15], [16], [17]. One of the most astonishing results of the QTMS radar experiment was that a “minimal” quantum radar can be very simple indeed. Unlike standard quantum illumination, QTMS radar requires only commercially available equipment for every component of the radar except the signal generator. It should come as no surprise, then, that the signal generator is by far the most difficult aspect of building a QTMS-type quantum radar. We will see that the requirements for this sort of signal generator constitutes one of the great challenges of quantum radar.
On the other hand, the QTMS radar experiment has given rise to voices asserting that quantum radar—or at least QTMS radar—has no practical application [5], [18], [19], [20], [21]. We refer the reader to those papers for a counterpoint to the arguments presented here.
In the previous section, we have seen that at least two classes of quantum radar rely on the quantum phenomenon known as entanglement. We will review those two classes next. But before we do so let us review what entanglement is—and is not.
There appears to be a perception among many people that entanglement is a sort of “spooky action at a distance” (to quote Einstein’s colorful phrase). It is said that if two particles are entangled, then whatever happens to one particle will happen to the other, no matter how far apart they are from each other. This is not a correct characterization of entanglement. Indeed, it violates a very basic law of physics, as shown by a simple thought experiment. Suppose we have two entangled pulses of light. Send one of them at a wall where it is completely absorbed. According to this mistaken description of entanglement, the other pulse of light would disappear from thin air. This violates conservation of energy! Therefore, entanglement cannot act as described.
A more correct explanation of entanglement is that two entangled particles must be described by a single quantum state. Although this is true, it is not a helpful characterization for the purposes of understanding a quantum radar.
It is better to think of entanglement in probabilistic terms. In quantum mechanics, a quantum system can be described by a family of probability distributions ${p}_{\alpha}{(x)}$ where ${\alpha}$ parameterizes the family. Each probability distribution describes the probability of obtaining a certain value for a physical quantity, such as polarization or voltage. (All the distributions ${p}_{\alpha}{(x)}$ can be obtained from a single linear operator called the density operator.) As is well known, two probability distributions ${p}_{1}{(x)}$ and ${p}_{2}{(y)}$ are independent if and only if their joint distribution satisfies ${p}_{1,2}{(}{x},{y}{)} = {p}_{1}{(}{x}{)}{p}_{2}{(}{y}{)}$. Two quantum systems are entangled when the joint distribution ${p}_{{(}{\alpha},{\beta}{)}}{(x,y)}$ of two quantum systems is not independent for all choices of ${\alpha}$ and ${\beta}$. As an example, consider the so-called two-mode squeezed vacuum state, which consists of two entangled electromagnetic beams. If one measures each beam using a photon counter (loosely, ${\alpha} = {\beta} = $ “photon number”), the resulting number of photons is exactly the same for each beam, even though the photon number itself is random: The two beams are perfectly correlated in photon number. If one used a heterodyne detector instead (${\alpha} = {\beta} = $ “voltages”), the measured voltages for the two beams would also be correlated. For nonentangled systems, there might be correlations in photon number or in voltages, but not in both. Thus, entanglement can be thought of as a type of “supercorrelation.”
Quantum interferometry is much like normal interferometry except that, instead of using a beamsplitter to split a single signal into the two paths of an interferometer, a quantum signal generator is used to produce a quantum state called a N00N state. This is an entangled state and takes its name from the fact that it is a superposition of two possibilities: either there are N photons in one path and zero photons in the other, or there are zero photons in the first path and N photons in the second. It can be shown that, when N photons are sequentially sent through an interferometer, the phase resolution scales as ${\sqrt{N}}$. A similar calculation shows that, when a laser pulse with a mean of N photons is used, the phase resolution also scales as ${\sqrt{N}}$. However, a N00N state can achieve a phase resolution that scales as N [1]. Clearly, when N is large, a quantum interferometer is much more sensitive than an interferometer that uses single photons or laser pulses. And when N00N states are used in a radar, the increased phase resolution would lead to an increased resolution in range because the phase accrued by a radar signal is directly proportional to the path length.
The main challenges of a quantum interferometric radar are twofold. First, N00N states are very difficult to generate, especially when N is large [22], [23]. This is particularly true at microwave frequencies. Second, N00N states are very fragile, so the sensitivity of a naïve implementation of quantum interferometry would degrade quickly in the presence of loss [24]. It may be possible to come up with modified quantum interferometry schemes which preserve an increased phase resolution even in the presence of significant loss, but the subject has not been explored very extensively in the literature.
These challenges imply a rather restricted application space for quantum interferometric radars. Long-range sensing, for instance, is probably ruled out. However, the application space is probably not empty. Biomedical sensing is one example where sensors detect at very short ranges, where signal loss is less of an issue. On the other hand, tissue imaging technologies could greatly benefit from the increase in resolution that a quantum interferometric radar could bring. In the short term, however, the difficulties inherent in quantum interferometry have had the effect of redirecting attention to another quantum radar scheme which is less challenging to implement.
Compared to quantum interferometric radar, quantum illumination is conceptually far closer to conventional radars. The basic idea is as follows:
Although the pioneers of quantum illumination did not explicitly draw the connection, this procedure is manifestly a variation of matched filtering. There are only two main differences. First, instead of using a copy of the transmit signal as a reference, an entangled twin is used instead. Second, the final step uses a quantum joint measurement instead of the conventional cross-correlation filter that a conventional radar would typically use.
Quantum illumination radars can be said to be quantum-enhanced at both the signal generator and the receiver. The enhancement in signal generation comes from the fact that it is impossible to produce a pair of electromagnetic signals whose waveforms are exact copies of each other. It may be objected that a beamsplitter could do this, but this is only true in the classical limit: A full quantum-mechanical calculation shows that a beamsplitter (or any other mechanism to copy a signal) must necessarily introduce “quantum noise.” This noise stems from the Heisenberg uncertainty principle and cannot be eliminated by any means. However, entanglement allows a workaround by causing a portion of the quantum noise between two signals to be correlated, increasing the fidelity of the signals to each other and leading to better matched filtering. On the other hand, the enhancement in the receiver comes from the quantum joint measurement, which takes optimum advantage of the entanglement in the transmitted signal. Thus, quantum illumination leads to better radar detection performance (in the sense of better ROC curves) compared to conventional radars.
One of the great strengths of quantum illumination is that it is robust against signal loss, especially when compared to quantum interferometry. Note the wording that we used in the final step of the quantum illumination protocol: “If the joint measurement indicates that the two signals were initially entangled…” There is no need for the received signal to be entangled with the reference signal. Indeed, free-space loss and atmospheric noise is almost always enough to break the entanglement. Rather, the question is whether the two signals were entangled at the transmitter, and the role of the joint measurement is to infer whether this was true or not. This makes quantum illumination much more robust than quantum interferometry.
The implementation of a quantum illumination radar faces two main challenges: The generation of an appropriate entangled signal and the implementation of the joint measurement. Of these, the joint measurement is by far the most onerous. We will postpone a discussion of the entangled signal generator to the next section, in which we discuss QTMS radar because the entangled signal is the same for both. Here, we will focus on the joint measurement. The reader will have noted that no particulars about the measurement were given previously. This is because the details are far too complicated to give here. In fact, Tan et al.’s initial article [4] described the measurement purely mathematically (in terms of infinite-dimensional linear operators), without discussing how such a measurement might be performed in practice. A method for implementing an appropriate measurement was found later [25], but as admitted in [5], it lies “well beyond the reach of available technology.” In other words, the full quantum illumination advantage cannot be achieved with currently available techniques, at least at microwave frequencies. However, quantum illumination experiments at optical frequencies has been performed [26], [27], [28].
In addition to the practical difficulty, there is also a conceptual difficulty with the requirement for a joint measurement. In order for this measurement to be meaningful, the reference signal must be stored until the corresponding transmitted signal arrives at the receiver. Thus, a quantum memory of some sort (or at least a delay line) is necessary. But how should the radar know when to release the reference signal from the memory so it can be jointly measured together with the received signal? If the required delay is known, then the range of the target must also be known, and the whole purpose of a radar is defeated. No experimentally feasible proposal for overcoming this problem has been suggested to date. This was one of the motivations for QTMS radar, which we will now describe.
QTMS radar is a simplified version of quantum illumination which comes, conceptually speaking, even closer to conventional radars than quantum illumination does. It uses an entangled signal generator, but the receiver setup is entirely conventional. Instead of a complicated quantum joint measurement, a QTMS radar simply performs heterodyne measurements on the received and reference signals. This is a considerable simplification because heterodyne receivers are already used in many conventional radars. Because of this simplification, QTMS radar cannot achieve detection performance as high as that of a standard quantum illumination radar. On the other hand, the simplified detection scheme means that there is no need to measure the two signals simultaneously, eliminating the need for quantum memories or delay lines. Each signal can be measured separately, and the results correlated using a digital signal processor as is done in conventional radars. In short, QTMS radar sidesteps all the complications associated with the quantum joint measurement by forgoing the quantum enhancement at the receiver and using conventional equipment instead. However, it retains a quantum enhancement at the transmit side because the entangled signals still lead to better matched filtering.
A simplified depiction of the QTMS radar described in [7] is shown in Figure 1. The receiver setup on the right-hand side is straightforward: One signal goes to an antenna to be transmitted at a target, while another signal is immediately digitized. A receiver then receives a signal from free space and digitizes that, too. The more interesting portion of Figure 1 is the transmitter setup on the left-hand side, which depicts the source of the entangled signals used in the radar. The source itself is called a Josephson parametric amplifier (JPA). It is housed in a dilution refrigerator which cools the JPA to the extremely low temperature of 7 mK. This is required because, otherwise, thermal noise would swamp the JPA and render it incapable of generating entanglement.
Figure 1. A simplified depiction of a QTMS radar. This figure was adapted from [29, Figure 4].
The requirement for cryogenic refrigeration is the main challenge faced by QTMS radars of the type shown here. The same requirement is also faced by quantum illumination radars, which use the same type of entangled signals. A dilution refrigerator is bulky (about the size of a small car) and consumes a significant amount of power (about 15 kW). Figure 2 shows the interior of a dilution refrigerator, giving an idea of its size. (Note that the figure does not include some components, such as the helium tanks.) The size and power requirements may be reduced as cryogenic technologies advance. Luckily, JPAs themselves are rather small, as seen in Figure 3, so multiple JPAs could fit into a single refrigerator.
Figure 2. The interior of a dilution refrigerator. The Josephson parametric amplifier is inside the cylinder at the bottom. This figure originally appeared in [29].
Figure 3. A Josephson parametric amplifier mounted on a printed circuit board. This figure originally appeared in [30].
Note that an operational QTMS radar need not look like the one described previously, complete with cryogenic refrigeration and JPAs. As long as an appropriate source for entangled signals is available, a QTMS radar can be built. Just as modern computers are not built using vacuum tubes, improved quantum technologies may make quantum radars more compact. For example, another approach for building a QTMS radar exploits the fact that entangled signals are easier to generate in the optical domain: It may be possible to use optical-to-microwave conversion to build an entangled source without the need for cryogenic refrigeration [31]. The experiment in [7] is only a starting point. It shows that QTMS radars can be built today, and the experiment is already informing future work in quantum radar design—see [32] for an example. But it does not follow that future quantum radars will look much like that in [7].
We have seen that quantum radar faces a number of challenges. However, it is equally clear that these challenges are not necessarily unsurmountable. For example, it is possible that the N00N states required by a quantum interferometric radar will become more readily available as quantum technologies progress. Moreover, by an appropriate choice of radar design, it is possible to sidestep certain challenges altogether. This is the case with QTMS radar, which overcomes all the problems associated with the quantum joint measurement in standard quantum illumination by replacing it with heterodyne measurements.
Since there are no fundamental barriers to building a quantum radar, it is appropriate to ask where they can be used. Clearly, a QTMS radar cannot fit on top of a car—dilution refrigerators are too bulky for that. But it may be possible to install quantum radars in hospitals, for instance. Hospitals already accommodate bulky equipment such as MRI machines. It is also worth mentioning that MRI machines can cost upward of US$1 million, and a quantum radar could potentially be built for less than that using current technology. Other ground-based applications for quantum radars are also possible.
One of the great advantages of quantum radars is that they work at inherently low powers while still being able to detect targets. The QTMS radar experiment, for example, operated at a power of –82 dBm [7]. Thus, a quantum radar would be extremely safe for biomedical sensing, even over long periods of time (e.g., continuous monitoring of hospital patients’ vital parameters). This could supplement previous work on the use of radars for biomedical sensing [33]; see also [34], [35]. If greater transmit powers are necessary, one can move to systems containing multiple quantum transmitters [36]; there are also ways to amplify entangled signals without breaking the entanglement [37]. Furthermore, if quantum interferometry were to be refined to the point where prototype quantum interferometric radars could be built, it is possible that the increased resolution sensitivity could be of use in biomedical sensing as well.
There is another advantage to radars that fall under the umbrella of quantum illumination, including QTMS radars. As mentioned earlier, the type of entangled state they use is called two-mode squeezed vacuum. It can be shown that each of the two signals in this entangled state look exactly like thermal noise; the entanglement appears only in the correlation between the signals. This fact, together with the low signal powers inherent to a quantum radar, means that the signals will not interfere with its surroundings. Therefore, radars based on such signals are suitable in airports and other situations where interference must be avoided.
In conclusion, we may say that quantum radar is worth investigating further. The field is still new, and many possibilities exist which are still in their infancy and which we have been unable to touch upon, for example, Rydberg receivers [38]. Many challenges still exist. However, at least some of these challenges can be overcome. If they can be overcome, quantum radars could open the door to improved detection performance, especially when signal powers need to be low or when spectrum is at a premium. There exist many possible applications of quantum radars, so they merit a dedicated research effort to make them practically useful.
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