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arXiv:2205.05441 · Advanced Quantum Technologies

Entanglement‐Enhanced Quantum Ranging in Near‐Earth Spacetime

Qianqian Liu, Cuihong Wen, Jiliang Jing, Jieci Wang

Published Aug 23, 2023• 4 citations
arXivHTMLPDF

Abstract

Abstract A quantum ranging protocol to determine the distance between an observer and a target in the near‐Earth curved spacetime is proposed. Unlike quantum illumination, the quantum ranging scheme utilizes multiple quantum hypothesis testing to simultaneously determine the presence and location of the target. The interest is in how the Earth's spacetime curvature influences photon propagation as well as the performance of the quantum ranging. It is found that the maximum potential advantage of the quantum ranging strategy in the curved spacetime outperforms its flat spacetime counterpart. It is shown that the number of transmitted modes can enhance the maximum potential advantage of the quantum ranging tasks. In contrast, the maximum potential advantage of quantum ranging cannot be significantly increased by dividing the range into multiple slices in the curved spacetime.

DOI
10.1002/qute.202300182

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Abstract A quantum ranging protocol to determine the distance between an observer and a target in the near‐Earth curved spacetime is proposed. Unlike quantum illumination, the quantum ranging scheme utilizes multiple quantum hypothesis testing to simultaneously determine the presence and location of the target. The interest is in how the Earth's spacetime curvature influences photon propagation as well as the performance of the quantum ranging. It is found that the maximum potential advantage of the quantum ranging strategy in the curved spacetime outperforms its flat spacetime counterpart. It is shown that the number of transmitted modes can enhance the maximum potential advantage of the quantum ranging tasks. In contrast, the maximum potential advantage of quantum ranging cannot be significantly increased by dividing the range into multiple slices in the curved spacetime.
Quantum illumination can utilize entangled light to detect the low-reflectivity target that is hidden in a bright thermal background. This technique is applied to the detection of an object in the curved spacetime of the Earth, in order to explore how the curvature of spacetime affects quantum illumination. It is found that the spatial quantum illumination with entangled state transmitter outperforms that with coherent-state transmitter in the near-Earth curved spacetime. Moreover, either the quantum illumination system or the coherent-state system is employed, and gravity can enhance the spacetime target detection by reducing the thermal signal at the receiver. Besides, our model in principle can be applied to microwave quantum illumination and thus provides, to some degree, a theoretical foundation for the upcoming spatial quantum radar technologies.
It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination, when first proposed, was surprising as the entanglement's benefit survived entanglement-breaking noise. Since then, many efforts have been devoted to study quantum sensing in noisy scenarios. The applicability of such schemes, however, is limited to a binary quantum hypothesis testing scenario. In terms of target detection, such schemes interrogate a single spatiotemporal resolution bin at a time, limiting the impact to radar detection. We resolve this binary-hypothesis limitation by proposing an entanglement-assisted quantum ranging protocol. By formulating a ranging task as a multiary hypothesis testing problem, we show that entanglement enables a 6-dB advantage in the error exponent against the optimal classical scheme. Moreover, the proposed ranging protocol can also be used to implement a pulse-position modulated entanglement-assisted communication protocol. Our ranging protocol reveals entanglement's potential in general quantum hypothesis testing tasks and paves the way toward a quantum-ranging radar with a provable quantum advantage.
While quantum illumination (QI) can offer a quantum-enhancement in target detection, its potential for per-forming target ranging remains unclear. With its capabilities hinging on a joint-measurement between a returning signal and its retained idler, an unknown return time makes a QI-based protocol difficult to realise. This paper outlines a potential QI-based approach to quantum target ranging based on recent developments in multiple quantum hypothesis testing and quantum-enhanced channel position finding (CPF). Applying CPF to time bins, one finds an upper-bound on the error probability for quantum target ranging. However, using energetic considerations, we show that for such a scheme a quantum advantage may not be proven with current mathematical tools.
Abstract Spacetime curvature of the Earth deforms wave packets of photons sent from the Earth to satellites, thus influencing the quantum state of light. We show that Gaussian steering of photon pairs, which are initially prepared in a two‐mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum steerability of the state increases for a specific range of height h and then gradually approaches a finite value with further increasing height of the satellite's orbit. Comparing with the peak frequency parameter, the Gaussian steering changes more for different squeezing parameters, while the gravitational frequency effect leads to quantum steering asymmetry between the photon pairs. In addition, we find that the influence of spacetime curvature on the steering in the Kerr spacetime is very different from the non‐rotating case because special relativistic effects are involved.
We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.
Abstract Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range.