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Electromagnetic waves

COMPARISON OF CORRELATION PERFORMANCE FOR VARIOUS MEASUREMENT SCHEMES IN QUANTUM BIPARTITE RADAR AND COMMUNICATION SYSTEMS

Rory A. Bowell, Matthew J. Brandsema, Ram M. Narayanan, Stephen W. Howell, Jonathan M. Dilger

Published Jan 1, 2022• 2 citations
Publisher

Abstract

Bipartite systems have become popular in emerging quantum radar and quantum communication systems.This paper analyzes the various correlation coefficients for different types of quantum radar measurement schemes, such as: (i) immediate detection of the idler photon events to be used in post-processing correlation with the signal photon events, (ii) immediate detection of the idler electric field to be used in post-processing correlation with the signal electric field, (iii) immediate detection of the idler quadratures to be used in post-processing correlation with the signal quadratures, and (iv) conventional analog correlation method of the optical parametric amplifier.The showcased results compare the performance of these different methodologies for various environmental scenarios.This work is important at developing the fundamentals behind quantum technologies that require covariance measurements and will permit more accurate selection of the appropriate measurement styles for individual systems.

DOI
10.2528/pier22022506

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Bipartite systems have become popular in emerging quantum radar and quantum communication systems.This paper analyzes the various correlation coefficients for different types of quantum radar measurement schemes, such as: (i) immediate detection of the idler photon events to be used in post-processing correlation with the signal photon events, (ii) immediate detection of the idler electric field to be used in post-processing correlation with the signal electric field, (iii) immediate detection of the idler quadratures to be used in post-processing correlation with the signal quadratures, and (iv) conventional analog correlation method of the optical parametric amplifier.The showcased results compare the performance of these different methodologies for various environmental scenarios.This work is important at developing the fundamentals behind quantum technologies that require covariance measurements and will permit more accurate selection of the appropriate measurement styles for individual systems.
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.
Quantum-based systems are an emerging topic of research due to their potential for increasing performance in a variety of classical systems.In radar and communication systems, quantum technologies have been explored in an effort to increase the correlation performance in the low signal-tonoise ratio (SNR) regime.While this increase has been shown both mathematically and in the laboratory using bipartite states, systems utilizing multi-partite squeezing and entanglement may lead to an even further performance increase.We investigate this by analyzing the correlation coefficient for a tripartite system electric field measurement to determine how it compares to the bipartite systems in the current literature for the same transmit powers.This is done by defining a tripartite wave function in terms of the mean photon number per mode then determining the covariance matrix from this wave function.This work is important in understanding how alternative states of light can be used for quantum radar applications.
Recently, much of the quantum radar/lidar research is focused on correlating single photon detection events with no delay line on the idler path. In other words, measuring the idler immediately, and correlating these events with later received photon events from the returning signal. This research approach has raised some questions due to the fact that all measurements done are classical, yet researchers are still observing sensor improvement in comparison to classical techniques. This therefore implies that the benefits from quantum radar/lidar using these techniques should be able to be explained entirely classically. This paper explores this concept by asserting that the correlation between the signals used in quantum remote sensing is largely due to the fact that the signal and idler photons are created simultaneously (which is only possible from an entangled source). We show, using very simple computer simulations, that having a single photon correlated (binary) waveform leads to correlation SNR advantages only in the low photon level regime, agreeing with previous literature.
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.
In recent years, quantum radar has focused entirely on using bipartite squeezed states of light as a mechanism for target detection. This paper studies the performance of a quantum radar that uses a tripartite squeezed state, whereby two signal beams are sent out towards the target which both correlate with the idler. It is found that for very low signal strengths, the bipartite has better performance. As the signal strength increases however, the tripartite becomes dominant. This result suggests that quantum radar (declared useful only in the low SNR regime) may possess more possibilities of increased performance at higher SNRs when different states are used for correlation. The bottleneck, of course, is the ability to generate transmit powers necessary to utilize.
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.