# Can quantum mechanics improve radar technology?

## Detecting targets with quantum entanglement might not be around the corner

Press reports allude regularly to a “quantum advantage” in the field of long range detection of hidden targets or threats, which would have a substantial impact for the military. We’re looking here at the science and conclude that, while long range applications of quantum radars are not exactly for tomorrow, it doesn’t mean that enhanced sensitivity through entanglement will not show practical advantages.

Radars are nowadays very common devices whose applications extend beyond their military origins and range from air and naval traffic surveillance, to weather forecasts, passing through the development of self-driving cars

The scope of a radar is to probe a region of space and to decide whether in this region is a target, e.g. an enemy aircraft, in its original defense application, or not. To achieve this goal, the radar emits electromagnetic radiation, usually in the microwave regime, towards the target region. If a target is there, some radiation will be reflected towards the radar. Detecting (or not) this reflected signal, the radar can decide if the target is present (or absent).

Formulated in these terms, the radar mission seems quite simple: it has to distinguish something from nothing. In practice, however, the radar problem is more complicated than that for two main reasons. First, during the radar-target-radar round trip, the transmitted radiation is significantly attenuated by propagation losses and low targets reflectivities. Second, every object of the environment with a finite temperature, including the atmosphere, emits radiation. This thermal radiation is particularly intense for microwaves, and induces what is called a thermal background at the detection stage. In other words, the radar receiver will always detect a strong signal, coming from this thermal background, whether or not the target is present.

Therefore, the radar mission is to search for a needle (the small reflected signal) in a haystack (the strong thermal background).

Fortunately, to face this very difficult problem, radar scientists can count on the powerful mathematical tools of **hypothesis testing**. Hypothesis testing is a branch of information theory which studies the optimal measurement strategy to distinguish between two hypotheses *H₀* (target absent) and *H₁* (target present). To quantify how good a measurement strategy is, it is useful to define the false alarm probability *Pf*, namely the probability of wrongly deciding that the target is present when it is not, and the detection probability *Pd*, namely the probability to correctly detect the target when it is present. There needs to be a trade-off between the optimization of both these quantities. For instance, if we blind the radar, there will never be any false alarm, but of course at the cost of no detection, which is not what we want. Thus, usually, one defines a maximal false alarm probability *Pf* that one can tolerate, and chooses the measurement strategy that maximize the detection probability *Pd*.

**An efficient strategy to increase the detection probability is to exploit correlations**. Namely, the radar sender generates two correlated beams, one is sent towards the target region, and the other is kept within the radar as a reference. The radar receiver will then compute the correlations between this reference and the radiation returning from the target region. As the thermal background is not correlated to the reference, the absence of correlation will be a signature of the absence of the target. On the contrary, **if some radiation is reflected from the target, this radiation is correlated with the retained one, and their correlations can be used to discriminate the weak reflected signal from the strong thermal background.**

While this strategy may sound very smart, unfortunately, quantum electromagnetic theory and hypothesis testing tell us that classical correlations are too weak. Indeed, light is composed of photons which for classical, or coherent, illumination are randomly distributed in arrival time.

This induces noise at the detection stage, called shot noise, which limits the amount of correlations that can be present between the reference beam and the one sent to the target.

One can show that using these classical correlations it is not possible to perform better than by simply sending all the available coherent radiation to the target and looking at the reflected light.

**Quantum mechanics, however, provides a particular form of correlations, called entanglement, which can be stronger than any possible classical correlations.** This concept of entanglement is unique to quantum objects and is at the heart, for instance, of quantum computing. It is therefore natural to ask the question if a quantum radar using entanglement can exploit these stronger correlations to overcome the performances of classical radar.

To give a quantitative answer to this question, let us consider how the probability of detection *Pd* of optimal classical and quantum radars change as a function of the signal-to-noise ratio (*SNR*) at different fixed levels of the false alarm probability *Pf* (see figure above). The *SNR* is defined as the ratio between the intensity of the microwave pulse returning from the target, and the intensity of the thermal background. Accordingly, a value of the *SNR* larger than unity represents the favorable condition of a return signal stronger than the background, but this condition is never verified in practice in the radar problem. On the other hand, when *SNR*< 1, we are in the radar-relevant regime of thermal background stronger than the signal. By comparing the red curves (corresponding to a quantum radar) with the blue ones (corresponding to a classical radar), **we see that there is a range of values of SNR for which a quantum radar provides a larger detection probability Pd than its classical analog**.

Unfortunately, while these curve seem very promising, applying this concept within the actual working regime of a radar is another story. Exhibiting the performances plotted in the figure above in an actual experiment faces technical limitations that researchers would need to overcome. In fact, for the quantum radar to work, one needs to preserve the retained microwave pulse until the return pulse reflected from the target comes back to the radar, and then perform a complex joint measurement which is able to resolve if quantum correlations between the two pulses are present or not.

However, no quantum radar experiment, up to today, has been able to perform such kind of measurement.

Even assuming that these technological issues will be solved (possibly in the near future) quantum radars still present a fundamental limitation. In fact, the extra correlations enabled by entanglement are significant only for extremely low power pulses. This causes the typical power of entangled microwave pulses to be of the order of a fraction of a femtowatt. On the other hand, when increasing the signal power the advantage of a quantum radar over a classical one completely vanishes. Such a limitation is overwhelming if we think at the high powers (typical radar powers range from few milliwatts to several kilowatts) that a real-life radar requires for standard long-range applications such as airplane tracking.

**We can therefore conclude that quantum radars would surely not replace standard long-range devices**. However, this technology may still prove useful in situations where one is forced to use very low powers (as it often happens in biological imaging) or to operate in very hot environments (e.g. an industrial furnace), but also in other quantum metrology areas one did not think of yet.

Thus, as often in basic science, even if ultimately quantum radar concepts will not be used in their original context, they will definitely participate to the emergence of highly innovative quantum technologies.

## The authors

**Giacomo Sorelli** and **Nicolas Treps **are researchers at the Laboratoire Kastler-Brossel and Sorbonne Université. Giacomo Sorelli is also affiliated with Onera — the French Aerospace Lab.

## To go further

This post is based on the authors’ paper *“**Detecting a target with quantum entanglement**”.* This review paper recollects the main advances in the quantum radar literature accompanied by a thorough introduction of the quantum optics background necessary for its in depth understanding. It includes further references.