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arXiv:2105.04527 · IET Quantum Communication

Classical benchmarking for microwave quantum illumination

Athena Karsa, Stefano Pirandola

Published Nov 25, 2021• 8 citations
arXivHTMLPDF

Abstract

Abstract Quantum illumination theoretically promises up to a 6 dB error‐exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime that includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well‐known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. This work outlines what is the true classical benchmark for the microwave Quantum illumination using coherent states, providing new bounds on error probability and closed formulae for the receiver operating characteristic, for both optimal (based on quantum relative entropy) and homodyne detection schemes. An alternative source generation procedure based on coherent states is also proposed, which demonstrates the potential to make classically optimal performances achievable in optical applications. The same bounds and measures for the performance of such a source are provided, and its potential utility in the future of room temperature quantum detection schemes in the microwave is discussed.

DOI
10.1049/qtc2.12025

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Abstract Quantum illumination theoretically promises up to a 6 dB error‐exponent advantage in target detection over the best classical protocol. The advantage is maximised by a regime that includes a very high background, which occurs naturally when one considers microwave operation. Such a regime has well‐known practical limitations, though it is clear that, theoretically, knowledge of the associated classical benchmark in the microwave is lacking. The requirement of amplifiers for signal detection necessarily renders the optimal classical protocol here different to that which is traditionally used, and only applicable in the optical domain. This work outlines what is the true classical benchmark for the microwave Quantum illumination using coherent states, providing new bounds on error probability and closed formulae for the receiver operating characteristic, for both optimal (based on quantum relative entropy) and homodyne detection schemes. An alternative source generation procedure based on coherent states is also proposed, which demonstrates the potential to make classically optimal performances achievable in optical applications. The same bounds and measures for the performance of such a source are provided, and its potential utility in the future of room temperature quantum detection schemes in the microwave is discussed.
Abstract Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal–idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification.
Broadly speaking, in quantum illumination we can say that a proposed protocol has a “quantum advantage” if it outperforms all possible classical protocols. In the optical domain of LIDAR, this is the most useful metric as lasers can routinely produce nearly ideal classical states of light at room temperature (RT). This is not the case in the microwave domain of RADAR where the photon energy is much less than the 300K thermal energy, meaning that a real RT microwave source will always be contaminated by significant thermal noise. Thus, it is not clear if it is technologically possible to produce an ideal classical microwave signal at RT. It is therefore interesting to ask if a microwave quantum illumination protocol can have a “practical advantage” compared to the best technologically feasible RT microwave source. In this paper, we look to frame this question more precisely. As a concrete example, we present experimental results showing that, contrary to recent claims in the literature [1], an entangled microwave source amplified by a cryogenic HEMT amplifier fails to obtain any performance advantage over a simply constructed RT source and, in facts, performs significantly worse. We present a simple theory which explains the experimental results and which offers guidance on how a practical advantage might be achieved.
Entanglement is vulnerable to degradation in a noisy sensing scenario, but surprisingly, the quantum illumination protocol has demonstrated that its advantage can survive. However, designing a measurement system that realizes this advantage is challenging since the information is hidden in the weak correlation embedded in the noise at the receiver side. Recent progress in a correlation-to-displacement conversion module provides a route towards an optimal protocol for practical microwave quantum illumination. In this work, we extend the conversion module to accommodate experimental imperfections that are ubiquitous in microwave systems. To mitigate loss, we propose amplification of the return signals. In the case of ideal amplification, the entire six-decibel error-exponent advantage in target detection error can be maintained. However, in the case of noisy amplification, this advantage is reduced to three decibels. We analyze the quantum advantage under different scenarios with a Kennedy receiver in the final measurement. In the ideal case, the performance still achieves the optimal one over a fairly large range of error probability with only on-off detection. Empowered by photon-number-resolving detectors, the performance is further improved and also analyzed in terms of receiver operating characteristic curves. Our findings pave the way for the development of practical microwave quantum illumination systems.
Quantum illumination has been suggested as a way to improve the sensitivity of remote target detection by taking advantage of quantum entanglement between a traveling electromagnetic beam of light interrogating the target, and a second beam kept in the lab. In the microwave domain, superconducting quantum circuit utilizing superconducting Josephson tunnel junctions can be used as quantum-limited amplifiers of faint microwave signals, as well as bright sources of quantum entangled signals. These Josephson parametric amplifiers (JPAs) are poised to become fundamental building block in a future quantum illumination radar operating in the microwave domain. Demonstrating a practical advantage of quantum illumination with ambient temperature signals is, however, challenging. Indeed, current quantum protocols are not practical as they require a complex receiver with stringent phase-matching conditions, which cannot be met in the field. Notably, it is also not currently known how one can transfer faint microwave signals out of cryogenic systems without destroying their fragile entanglement. In this article, we discuss the recent progress and challenges regarding the development of an all-microwave quantum illumination radar using the recently developed and implemented quantum-enhanced noise radar protocol. This quantum illumination protocol is simpler to implement and procures a quantum enhancement over its classical analog. Finally, we discuss different strategies that may resolve the issue of transmitting microwave entanglement under ambient conditions. We, thus, conclude that successful transmission of entangled microwaves can be done in the near future, with possible demonstrations of practical quantum advantage over short distances.
Quantum illumination is a sensing technique that employs entangled signal-idler beams to improve the detection efficiency of low-reflectivity objects in environments with large thermal noise. The advantage over classical strategies is evident at low signal brightness, a feature which could make the protocol an ideal prototype for non-invasive scanning or low-power short-range radar. Here we experimentally investigate the concept of quantum illumination at microwave frequencies, by generating entangled fields using a Josephson parametric converter which are then amplified to illuminate a room-temperature object at a distance of 1 meter. Starting from experimental data, we simulate the case of perfect idler photon number detection, which results in a quantum advantage compared to the relative classical benchmark. Our results highlight the opportunities and challenges on the way towards a first room-temperature application of microwave quantum circuits.
Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Here, we describe and analyze a system for applying this technique at microwave frequencies, a more appropriate spectral region for target detection than the optical, due to the naturally occurring bright thermal background in the microwave regime. We use an electro-optomechanical converter to entangle microwave signal and optical idler fields, with the former being sent to probe the target region and the latter being retained at the source. The microwave radiation collected from the target region is then phase conjugated and upconverted into an optical field that is combined with the retained idler in a joint-detection quantum measurement. The error probability of this microwave quantum-illumination system, or quantum radar, is shown to be superior to that of any classical microwave radar of equal transmitted energy.