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Radar Sensor Technology

Electric field correlations in quantum radar and the quantum advantage

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

Published Apr 23, 2020• 8 citations
Publisher

Abstract

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.

DOI
10.1117/12.2562749

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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.
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.
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.
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-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.
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.