Detection and Estimation in Quantum Illumination

Abstract

Quantum radar exploits the properties of quantum entanglement to enhance its performance over classical radar. Quantum illumination, being one special type of quantum radar, generates a pair of highly entangled beams called the signal and idler beams, transmits the signal beam for target exploration, and examines the returned signal beam using the quantum entanglement to improve the target detection and estimation performance. In this thesis, the role of the optical parametric amplifier (OPA) in target detection of the QI system is first studied. We propose a dual-OPA design of the detector so that an optimum combination of intensities of inputs can be achieved, yielding a marked improvement in the detector performance. The information of the entanglement contained in the covariance matrix (CM) between the returned signal and idler beams is then considered. Here, we propose a technique that exploits the entanglement to a higher degree. This detection method employs the metric of Riemannian distances (RD) between the reconstructed CMs as the test statistic to assess the probabilities of “target” or “no target”. Numerical experiments confirm that the CM detector is far superior in detection performance to the OPA detectors. We then turn our attention to the study of multi-parameter estimation problem in QI. Here, we focus our consideration on the simultaneous estimation of the target range and target velocity the information of which is embedded in the arrival time and frequency of the returned signal. The Quantum Cramer-Rao bound (QCRB) for the estimation of such parameters of the signal photon propagated through a random environment is derived. To facilitate the simultaneous estimation of the two parameters, we propose two methods. The first is a modified application of the classical ambiguity function in classical radar systems to the QI system. Analysis shows direct application of the classical ambiguity function may lead to multiple estimates of the desired parameters. Thus, we try to reconstruct the temporal wavefunctions of the returned signal and idler photons using interferometric measurement. The correlation of the wavefunctions with the reference signal at different time delays provides an estimate of the average arrival time of the return signal. In addition, the phase slopes yield an estimate of the central frequencies, thus completing the joint estimation of the two parameters. Seeing that the reconstruction of the wavefuctions requires a large amount of measurement data, we develop a second estimation method which applies a unitary operator at one end, and its inverse at the other end, of the QI system. The re-entangled returned signal beam and the idler beam both contain information of the two parameters and their estimation is carried out by measurements on the signal beam and on the idler beam respectively. Numerical experiments verify the validity and accuracy of these methods.