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arXiv:2008.12711 · IEEE Radar Conference (RadarConf)

A comparison between quantum and classical noise radar sources

Robert Jonsson, Roberto Di Candia, Martin Ankel, Anders Strom, Goran Johansson

Published Sep 21, 2020• 15 citations
arXivHTMLPDF

Abstract

We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons NStransmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of √2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/NS) larger than the optimal classical setup, in the NS<; <; 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.

DOI
10.1109/radarconf2043947.2020.9266597

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We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons NStransmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of √2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/NS) larger than the optimal classical setup, in the NS<; <; 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.
We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons N-S transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of root 2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/N-S) larger than the optimal classical setup, in the N-S << 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.
Quantum radar is an emerging technique, currently at the experimental stage, that promises to disrupt the well-established field of conventional radar. Recent progress shows that it is possible to generate and use entangled pairs of microwave photons for detection purposes and to obtain an advantage over a classical radar. In this work, we study the currently experimentally feasible type of quantum correlation radar. To this end, we compare different radar architectures, quantum and classical, by analyzing their detection performances by means of the receiver operating characteristic (ROC), the minimum error probability as well as the Chernoff bound. The underlying system models are based on quantum mechanical formulations as well as conventional signal theory. Where it is appropriate and necessary to facilitate our analysis, we apply the central limit theorem to establish the Gaussianity of the observable quantities. A conceptual analogy between the quantum and classic points-of-view is drawn and supported by results showing the asymptotic behavior of the ROC curves of both physical descriptions depending on the power levels of signal and noise. We come to exact and comprehensible conclusions on the current state of quantum radar in comparison to classic radar with a detailed mapping of the radar operating regime (measurement time, signal-to-noise ratio, environmental noise level, target object size and distance) in which a quantum advantage is attainable.
At the current state of the scientific discourse on quantum radar, the best understood and experimentally feasible types of implementation are based on two-mode-squeezed-vacuum photon states and aimed at the task of target detection. The operating environment, in which an advantage over classical radar may be attainable, is thereby limited to the extreme regimes of very low signal-to-noise ratios and high thermal noise levels as well as confining the required hardware at mK temperatures. In this work, we approach the open question of how to optimally operate a potential quantum radar system. To this end, we define the optimal operation by means of the detection advantage against classical radar as well as the efficient usage of the resource measurement time. We show that there is a trade-off between time-efficiency and out-performance of classical radar and specify the conditions for such an operation. Building on this aspect, we investigate the concept of the fair classical comparison to facilitate the understanding of its relation to quantum radar.
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.
We propose a protocol for quantum illumination: a quantum-enhanced noise radar. A two-mode squeezed state, which exhibits continuous-variable entanglement between so-called signal and idler beams, is used as input to the radar system. Compared to existing proposals for quantum illumination, our protocol does not require joint measurement of the signal and idler beams. This greatly enhances the practicality of the system by, for instance, eliminating the need for a quantum memory to store the idler. We perform a proof-of-principle experiment in the microwave regime, directly comparing the performance of a two-mode squeezed source to an ideal classical noise source that saturates the classical bound for correlation. We find that, even in the presence of significant added noise and loss, the quantum source outperforms the classical source by as much as an order of magnitude.
In this paper, we derive the electric field covariance matrix of the signal and idler beams from an entangled source for applications involving quantum radar. We also derive the corresponding covariance matrix for a classical matched filtering remote sensing system and compare to the quantum result. We use this comparison to derive an expression for the quantum enhancement factor as a function of the mean photon number per mode, Ns. This result is significant because it allows one to exactly calculate the predicted quantum enhancement as a function of transmit power, rather than only having an upper bound. Additionally, we look into previous analog correlation techniques using an optical parametric amplifier (OPA) and show that immediately detecting the idler produces the same cross correlation terms. However, the actual measurements needed to harness these correlations is enhanced when one immediately detects the idler because it minimizes the added noise caused by the additional length of the idler path in the conventional method. Finally, our results also show that one does not need to count photons to harness these correlations, but rather, perform electric field measurements.