## Abstract

Quantum illumination uses entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. Its advantage is particularly evident at low signal powers, a promising feature for applications such as noninvasive biomedical scanning or low-power short-range radar. Here, we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields to illuminate a room-temperature object at a distance of 1 m in a free-space detection setup. We implement a digital phase-conjugate receiver based on linear quadrature measurements that outperforms a symmetric classical noise radar in the same conditions, despite the entanglement-breaking signal path. Starting from experimental data, we also simulate the case of perfect idler photon number detection, which results in a quantum advantage compared with the relative classical benchmark. Our results highlight the opportunities and challenges in the way toward a first room-temperature application of microwave quantum circuits.

## INTRODUCTION

Quantum sensing is well developed for photonic applications (*1*) in line with other advanced areas of quantum information (*2*–*5*). Quantum optics has been, so far, the most natural and convenient setting for implementing the majority of protocols in quantum communication, cryptography, and metrology (*6*). The situation is different at longer wavelengths, such as tetrahertz or microwaves, for which the current variety of quantum technologies is more limited and confined to cryogenic environments. With the exception of superconducting quantum processing (*7*), no microwave quanta are typically used for applications such as sensing and communication. For these tasks, high-energy and low-loss optical and telecom frequency signals represent the first choice and form the communication backbone in the future vision of a hybrid quantum internet (*8*–*10*).

Despite this general picture, there are applications of quantum sensing that are naturally embedded in the microwave regime. This is exactly the case with quantum illumination (QI) (*11*–*17*) for its remarkable robustness to background noise, which, at room temperature, amounts to ∼10^{3} thermal quanta per mode at a few gigahertz. In QI, the aim is to detect a low-reflectivity object in the presence of very bright thermal noise. This is accomplished by probing the target with less than one entangled photon per mode, in a stealthy noninvasive fashion, which is impossible to reproduce with classical means. In the Gaussian QI protocol (*12*), the light is prepared in a two-mode squeezed vacuum state (*3*) with the signal mode sent to probe the target, while the idler mode is kept at the receiver. Although entanglement is lost in the round trip from the target, the surviving signal-idler correlations, when appropriately measured, can be strong enough to beat the performance achievable by the most powerful classical detection strategy. In the low photon flux regime, where QI shows the biggest advantage, it could be suitable for extending quantum sensing techniques to short-range radar (*18*) and noninvasive diagnostic scanner applications (*19*).

Previous experiments in the microwave domain (*20*, *21*) demonstrated a quantum enhancement of the detected covariances compared with a symmetric classical noise radar, i.e., with approximately equal signal and idler photon number. With appropriate phase-sensitive detection, an ideal classically correlated noise radar can be on par or, in the case of a bright idler (*17*), even outperform coherent heterodyne detection schemes, which maximize the signal-to-noise ratio (SNR) for realistic (phase-rotating) targets. However, if the phase of the reflected signal is stable over relevant time scales or a priori known, then homodyne detection represents the strongest classical benchmark.

In this work, we implement a digital version of the phase-conjugate receiver of (*22*), experimentally investigating proof-of-concept QI in the microwave regime (*23*). We use a Josephson parametric converter (JPC) (*24*, *25*) inside a dilution refrigerator for entanglement generation (*26*, *27*). The generated signal microwave mode, with annihilation operator *28*–*30*). This enables an implementation of the phase-conjugate receiver that fully exploits the correlations of the JPC output fields without analog photodetection. We then compare the SNR with other detection strategies for the same signal path, i.e., the same signal photon numbers at the JPC output, which is also our reference point for the theoretical modeling.

Our digital approach to QI circumvents common practical problems such as finite idler storage time that can limit the range and fidelity of QI detection schemes. However, this advantage comes at the expense that the theoretically strongest classical benchmark in the same conditions—the coherent-state homodyne detector using the same signal power and signal path—can be approached in specific conditions such as quantum-limited amplification, but never be outperformed. To outperform coherent-state homodyne detection in practice, we will require low-temperature square law detection of microwave fields that can be realized with radiometer or photon counting measurements. Nevertheless, using calibration measurements of the idler path, we can simulate a situation with perfect idler photon number detection, extrapolating the case where the reflected mode is detected together with the idler mode using analog microwave photon counters. For this situation, we show that the SNR of coherent heterodyne detection and symmetric noise radars is exceeded by up to 4 dB and that of homodyne detection—the classical benchmark—by up to 1 dB for the same amplified signal path, measurement bandwidth, and signal power. We also note that the strong and noisy amplification of the signal path chosen to facilitate the detection with commercial analog-to-digital converters enables another classical receiver strategy, i.e., the detection of the amplifier noise in the presence of the target. Since the amplified noise exceeds the environmental noise at room temperature by orders of magnitude, this would be the most effective strategy for the implemented experiment. For the same reason, a low-noise coherent source at room temperature would outperform the relative benchmarks considered here. In practice, outperforming the room temperature benchmark depends on the chosen amount of gain, the type of amplifier, and the loss in the detection system and therefore does not pose a fundamental limitation to the presented measurement scheme that focuses on the relative comparison of the different illumination types.

## RESULTS

The experimental setup, shown in Fig. 1B, is based on a frequency tunable superconducting JPC operated in the three-wave mixing regime and pumped at the sum of signal and idler frequencies ω_{p} = ω_{S} + ω_{I}; see Materials and Methods for more details. The output of the JPC contains a nonzero phase-sensitive cross-correlation _{S} = 10.09 GHz and the idler mode with frequency ω_{I} = 6.8 GHz. In our work, the quantities *I _{i}* and

*Q*, which are related to the complex amplitudes

_{i}*a*and their conjugate

_{i}*R*= 50 ohms,

*B*= 200 kHz is the measurement bandwidth set by a digital filter, and

*i*= S, I (

*30*–

*32*). We calibrate the system gain (

*G*

_{S},

*G*

_{I}) = (93.98(01),94.25(02)) dB and system noise (

*n*

_{add, S},

*n*

_{add, I}) = (9.61(04),14.91(1)) of both measurement channels as described in Materials and Methods.

A first important check for the experiment is to quantify the amount of entanglement at the output of the JPC at 7 mK. A sufficient condition for the signal and idler modes to be entangled is the nonseparability criterion *33*), for the joint field quadratures _{S} and idler ω_{I} frequencies, and fed to the JPC inside the dilution refrigerator. Note that, for both JPC and classically correlated noise, we digitally rotate the relative phase of the quadratures to maximize the correlation between signal and idler.

The classically correlated signal and idler modes are then reflected back from the JPC (pumps are off) and pass through the measurement lines attached to the outputs of the JPC. This ensures that both classical and quantum radiations experience the same conditions in terms of gain, loss, and noise before reaching the target and before being detected in the identical way. As shown in Fig. 2A, at low photon number, the parameter Δ is below one, proving that the outputs of the JPC are entangled, while at larger photon number (larger pump power), the entanglement gradually degrades and vanishes at *N*_{S} = 4.5 photons s^{−1} Hz^{−1}. We attribute this to finite losses in the JPC, which leads to pump power–dependent heating and results in larger variances of the output field. The classically correlated radiation of the same signal power, on the other hand (orange data points), cannot fulfill the nonseparability criterion, and therefore, Δ ≥ 1 for the entire range of the signal photons. In the latter case, we also observe a slow relative degradation of the classical correlations as a function of the signal photon numbers, which could be improved with more sophisticated noise generation schemes (*20*).

The experiments of QI and classically correlated illumination (CI) are implemented in a similar way (see Fig. 1B). The two amplified quadratures of the idler mode *i* = 1) or absence (*i* = 0) of the object is then postprocessed for the reconstruction of the covariance matrix of the detected signal-idler state.

The signal mode *n*_{det, S} is the amplifier-added noise after interrogating the object region. In the presence of the target and for η ≪ 1, the added noise to the signal is *n*_{env} as well as the signal photon numbers used to probe the target.

This implies that, in our proof-of-principle demonstration, the optimal classical strategy would actually be based on detecting the presence or absence of the amplifier noise rather than the coherences and correlations of the signal-idler path with the measured SNR_{passive} = (*n*_{1} − *n*_{0})/(*n*_{0} + 1) ≃ 31.4 dB for the chosen gain and receiver noise in our setup. However, for lower-noise-temperature signal amplifiers and lower gain, as well as in longer range applications with increased loss, such a passive signature of the detection scheme will be markedly reduced and eventually disappear in the environmental noise at room temperature.

The final step of the measurement is the application of a digital version of the phase-conjugate receiver (*22*). The reflected mode *i* = 0) and the presence (*i* = 1) of the target (here,

The experiment of coherent-state illumination is performed by generating a weak coherent tone using a microwave source at room temperature, followed by a low-temperature chain of thermalized attenuators inside the dilution refrigerator. The center frequency of the coherent tone is ω_{S}, exactly matched with the frequency of the signal used in the QI and CI experiments. The coherent tone is reflected back from the unpumped JPC and directed into the same measurement chain identical to that of QI and CI (see Fig. 1B). The signal is sent to probe a target region, and the detected radiation

In the absence of a passive signature due to signal noise amplification, digital homodyne detection of a coherent state represents the optimal classical strategy in terms of the SNR, which is given by

In Fig. 2B, we compare the SNR of QI and CI with and without idler calibration for a perfectly reflective object in a zero loss channel η = 1. For comparison, we also include the results of coherent-state illumination with homodyne and heterodyne detection. In all cases, the signal mode at room temperature is overwhelmed with amplifier noise. We use three sets of measurements to calculate the SD of the mean SNR of a single mode measurement with measurement time *T* = 1/*B* = 5 μs. Each set is based on *M* = 380,000 samples (192,000 for the coherent-state detection), corresponding to a measurement time of 1.87 s (0.93 s for the coherent-state detection). To get the total statistics, the measurement time takes 5.6 s (2.8 s for the coherent-state detection). For the same measurement bandwidth and using the raw data of the measured quadrature pairs (solid lines), QI (blue dots) outperforms suboptimum symmetric CI (orange dots) by up to 3 dB at low signal photon numbers, but it cannot compete with the SNR obtained with coherent-state illumination (yellow and green dots). Under the assumption of perfect idler photon number detection, i.e., applying the calibration discussed above (dashed lines), the SNR of QI is up to 4 dB larger than that of symmetric CI and coherent-state illumination with heterodyne detection, which does not require phase information, over the region where the outputs of the JPC are entangled. For signal photon numbers *N*_{S} > 4.5, where there is no entanglement present in the signal source, the sensitivity of the coherent-state transmitter with heterodyne detection outperforms QI and CI, confirming the critical role of entanglement to improve the sensitivity of the detection.

QI with a phase-conjugate receiver is potentially able to outperform coherent-state illumination with homodyne detection by up to 3 dB, i.e., the optimum classical benchmark, in the regime of low signal photon numbers. In the region *N*_{S} < 0.4, the experimentally inferred SNR of QI is approximately 1 dB larger, in agreement with the theoretical prediction taking into account experimental nonidealities like the finite squeezing of the source. In practice though, i.e., without the applied idler calibration, the quantum advantage compared with coherent homodyne detection is not accessible with a digital receiver based on heterodyne measurements, even in the case of quantum limited amplifiers, due to the captured idler vacuum noise, which lowers the optimal SNR by at least 3 dB (*12*, *16*). The experimental results (dots) are in very good agreement with the theoretical prediction (solid and dashed lines). For the theory, we rewrite the SNRs Eqs. 3 to 5 in terms of the signal photon number

An important feature of a radar or short-range scanner is its resilience with respect to signal loss. To verify this, as shown in Fig. 1B, we use two microwave switches at room temperature in the signal line to select between a digitally controllable step attenuator to mimic an object with tunable reflectivity and a proof-of-principle radar setup. With this setup, we determine the effects of loss and object reflectivity as well as target distance on the efficiency of the quantum enhanced radar. In Fig. 3A, we plot the measured SNR of QI, CI, and coherent-state illumination with heterodyne detection as a function of the imposed loss on the signal mode. The calibrated QI protocol is always superior to calibrated symmetric CI and coherent-state illumination with heterodyne detection for a range of effective loss −25 dB <η < 0 dB. The dashed lines are the theory predictions from Eqs. 3 and 5 for a fixed chosen signal photon number *N*_{S} = 0.5. The shaded regions represent the confidence interval extracted from the SD of the measured idler photon numbers, and the cross-correlations as a function of η.

In the context of radar, small improvements in the SNR lead to the exponentially improved error probability *M* = *T*_{tot}*B* is the number of single mode measurements, and *T*_{tot} is the total measurement time required for a successful target detection. To test the principle of microwave QI in free space at room temperature, we amplify and send the microwave signal emitted from the JPC to a horn antenna and a copper plate representing the target at a variable distance. The reflected signal from this object is collected using a second antenna of the same type, down converted, digitized, and combined with the calibrated idler mode to calculate the SNR of the binary decision. With this setup, we repeat the measurement for CI and coherent-state illumination with heterodyne. Figure 3B shows the SNR of these protocols as a function of the object distance from the transmitting antenna as well as the total loss of the free space link. Calibrated QI reveals higher sensitivity for a reflective target up to 1 m away from the transmitting antenna. The results are in good agreement with the theoretical model.

## DISCUSSION

In this work, we have studied proof-of-concept QI in the microwave domain, the most natural frequency range for target detection. Assuming perfect idler photon number detection, we showed that a quantum advantage is possible despite the entanglement-breaking signal path. Since the best results are achieved for less than one mean photon per mode, our experiment indicates the potential of QI as a noninvasive scanning method, e.g., for biomedical applications, imaging of human tissues, or nondestructive rotational spectroscopy of proteins, besides its potential use as short-range low-power radar, e.g., for security applications. However, for this initial proof-of-principle demonstration, the amplified bright noise in the target region overwhelms the environmental noise by orders of magnitude, which precludes the noninvasive character at short target distances and presents an opportunity to use the presence or absence of the amplifier noise to detect the object with even higher SNR. The use of quantum-limited parametric amplifiers (*34*–*36*) with limited gain, such that the amplified vacuum does not significantly exceed environmental or typical electronic noise at the target, will help to achieve a practical advantage with respect to the lowest-noise-figure coherent-state heterodyne receivers at room temperature, and, up to the vacuum noise, they will also render the idler calibration obsolete. The use of sensitive radiometers or microwave single-photon detectors (*37*–*39*), at millikelvin temperatures without signal amplification, represents a promising route to achieve an advantage in practical situations and with respect to ideal coherent-state homodyne receivers. One advantage of the presented digital implementation of QI is that it does not suffer from the idler storage problem of receivers that rely on analog photodetection schemes, inherently limiting the accessible range when used as a radar. It is an interesting open question what other types of receivers (*40*) could be implemented in the microwave domain, based on the state-of-the-art superconducting circuit technology and digital signal processing.

## MATERIALS AND METHODS

### Josephson parametric converter

We use a nondegenerate three-wave mixing JPC that acts as a nonlinear quantum-limited amplifier whose signal, idler, and pump ports are spatially separated, as shown in Fig. 4. The nonlinearity of the JPC originates from a Josephson ring modulator (JRM) consisting of four Josephson junctions arranged on a rectangular ring and four large shunting Josephson junctions inside the ring (*41*). The total geometry supports two differential and one common mode. The correct bias point is selected by inducing a flux in the JRM loop by using an external magnetic field. The two pairs of the microwave half-wavelength microstrip transmission line resonators connected to the center of JRM serve as signal and idler microwave resonators. These resonators are coupled to two differential modes of the JRM and capacitively attached to two external feedlines, coupling in and out the microwave signal to the JPC.

The entanglement between signal mode with frequency ω_{S} and idler mode with frequency ω_{I} is generated by driving the nonresonant common mode of the JRM at frequency ω_{p} = ω_{I} + ω_{S}. Two off-chip, broadband 180° hybrids are used to add the idler or signal modes to the pump drive. In our configuration, we apply the pump to the idler side and terminate the other port of the signal hybrid with a 50-ohm cold termination. The frequency of the signal mode is ω_{S} = 10.09 GHz, and the frequency of the idler mode is ω_{I} = 6.8 GHz. The maximum dynamical bandwidth and gain of our JPC are 20 MHz and 30 dB, respectively. The 1-dB compression point corresponds to the power −128 dBm at the input of the device at which the device gain drops by 1 dB and the amplifier starts to saturate. The frequency of the signal and idler modes can be varied over the 100-MHz span by applying a direct current to the flux line.

### Noise calibration

The system gain *G _{i}* and system noise

*n*

_{add, i}of both signal and idler measurement chains are calibrated by injecting a known amount of thermal noise using two temperature-controlled 50-ohm cold loads (

*26*,

*42*). The calibrators are attached to the measurement setup with two copper coaxial cables of the same length and material as the cables used to connect the JPC via two latching microwave switches (Radiall R573423600). A thin copper braid was used for weak thermal anchoring of the calibrators to the mixing chamber plate. By measuring the noise density in V

^{2}/Hz at each temperature as shown in Fig. 5 and fitting the obtained data with the expected scaling

*B*= 200 kHz and

*R*= 50 ohms, we accurately back out the total gain

The 95% confidence values are taken from the standard error of the fit shown in Fig. 5.

### Measurement chain: Gain and added noise

In Fig. 6, we show the full measurement chain used in our experiment. The outputs of the JPC, the signal *i* = S, I is the annihilation operator of the noise mode added by the HEMT and one additional room temperature amplifier and the preceding cable and connector losses. The idler mode is then down converted to 20 MHz, filtered, amplified using an amplifier with gain

The signal mode is used to probe the target region. The reflected signal from the target region in the presence *H*_{1} or absence *H*_{0} of the target, respectively, is given by

The signal mode after down conversion is given by*i* = 0,1,

### Digital postprocessing

In this section, we explain how the single-mode postprocessing was performed. As shown in Fig. 7A, the down-converted and amplified signal and idler modes are continuously recorded with 100 MS/s using a two-channel ADC with 8-bit resolution. The total measurement time of the QI/CI detections (coherent-state detections) is 5.76 s (2.88 s) in which the recorded data are chopped to *M* = 1.15 × 10^{6} (6 × 10^{5}) records; each contains 500 samples, which corresponds to a filter bandwidth of 200 kHz. The 500 samples are used to perform FFT on each record individually and extract the complex quadrature voltages *I*_{I}, *Q*_{I} and *I*_{S}, *Q*_{S} of the intermediate frequency component at 20 MHz. We calculate the detected field quadratures of both signal and idler modes *i* = S, I for *M* measurement results, which have the same measurement statistics as the quadrature operators

### Digital phase-conjugate receiver: QI and CI

Both the JPC and a correlated classical source generate a zero-mean, two-mode Gaussian state with a nonzero cross correlation *M* copies of the measurement results with the statistics of

The target absence-or-presence decision is made by comparing the difference of the two detectors’ total photon counts (*23*), which is equivalent to the measurement of the operator*M*, the central limit theorem implies that the measurement of *i* = 0,1, being the conditional means and conditional variances of *M* copies. For the reported raw SNR, we use Eq. 19 without any calibration applied. To infer the hypothetical SNR that could be obtained with access to the idler mode directly at the JPC output *22*)*i* = 0,1, where we take the calibrated noiseless idler photon number

### SNR of the coherent-state illumination: Heterodyne and homodyne measurements

To perform the coherent-state illumination, we generate a coherent signal at room temperature and send it into the dilution refrigerator, where the mode *M* measurement results of the field quadrature operators

For the digital homodyne detection, we use phase information to rotate the signal to the relevant quadrature direction and obtain the improved SNR

This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## REFERENCES AND NOTES

**Acknowledgments:**We thank C. Wilson and, in particular, J. Shapiro for the helpful critical comments and discussions. We thank IBM for donating the JPC used in this work, J. Chow and B. Abdo for the helpful advice, as well as M. Labendik and R. Sett for their contribution to characterizing the JPC properties.

**Funding:**This work was supported by the Institute of Science and Technology Austria (IST Austria), the European Research Council under grant agreement number 758053 (ERC StG QUNNECT), and the E.U.’s Horizon 2020 research and innovation programme under grant agreement number 862644 (FET Open QUARTET). S.B. acknowledges support from the Marie Skłodowska Curie fellowship number 707438 (MSC-IF SUPEREOM); D.V. acknowledges support from E.U.’s Horizon 2020 research and innovation programme under grant agreement number 732894 (FET Proactive HOT) and the Project QuaSeRT funded by the QuantERA ERANET Cofund in Quantum Technologies; and J.M.F. from the Austrian Science Fund (FWF) through BeyondC (F71), a NOMIS foundation research grant, and the E.U.’s Horizon 2020 research and innovation programme under grant agreement number 732894 (FET Proactive HOT).

**Author contributions:**S.B., S.P., and D.V. proposed and developed the theoretical idea. S.B. and J.M.F. conceived the experiment, built the experimental setup, and analyzed the data. S.B. performed the theoretical calculation and the measurements. All authors contributed to the manuscript.

**Competing interests:**The authors declare that they have no competing interests.

**Data and materials availability:**The data and code used to produce the results of this manuscript are available on Zenodo: https://doi.org/10.5281/zenodo.3745579.

- Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).