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arXiv:2405.09571 · Physical Review Research

Optimal radar ranging pulse to resolve two reflectors

Andrew N. Jordan, John C. Howell, Achim Kempf, Shunxing Zhang, Derek White

Published Sep 27, 2024• 5 citations
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Abstract

Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar []. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength, leveraging results in quantum metrology. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse and their variants. Using orthogonal function theory, we give an explicit algorithm to optimize the wave pulse in finite time to have the best performance. We also explore range resolution estimation with unnormalized waveforms with multiparameter methods to also independently estimate loss and time of arrival. These results are consistent with the earlier single parameter approach of range resolution only and give deeper insight into the ranging estimation problem. Experimental results are presented using radio pulse reflections inside coaxial cables, showing robust range resolution smaller than a tenth of the inverse bandlimit, with uncertainties close to the derived Cramér-Rao bound. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033341

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Quantum radar (QR) has been shown to provide enhanced performance in target detection and parameter estimation, while its resolution capability remains largely unexplored. In classical radar theory, the ambiguity function is used to characterize waveform resolution capability. However, the volume invariance of the ambiguity function and the uncertainty relation of the Fourier transform impose fundamental limitations on the resolution capability of any single waveform. In this paper, we extend the idea of waveform ambiguity function to QR systems, thereby developing a quantum ambiguity function (QAF) that enables the evaluation of the ultimate resolution of quantum states and serves as a guide for quantum state design. We show that quantum entanglement reduces the volume of the QAF and increases the time- bandwidth product, thereby overcoming these classical limitations. Furthermore, by drawing an analogy to classical waveform modulation, we show how modulating entangled states can further improve resolutions and elucidate the underlying mechanisms of these improvements.
Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.
The quantum Cramér-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same time are not known. In this paper, we ascertain these optimal measurements for an arbitrary point spread function, in the most relevant regime of a small separation between the sources. Our measurement can be adjusted within a set of tradeoffs, allowing more information to be extracted from the separation or the centroid while ensuring that the total information is the maximum possible. Published by the American Physical Society 2024
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