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arXiv:2310.18610

Optical ranging with quantum advantage

Sankar Davuluri, Greeshma Gopinath, Matthew J. Woolley

Published Oct 28, 2023• 0 citations
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Abstract

The quantum illumination technique requires joint measurement between the idler and the probe reflected from the low-reflective target present in a noisy environment. The joint measurement is only possible with prior knowledge about the target's location. The technique in this article overcomes this limitation by using entanglement and a cross-correlated homodyne measurement. This technique does not require quantum storage of the idler and prior knowledge about the target's distance. The cross-correlation measurement makes this technique completely immune to environmental noise, as the correlation between the idler and the environment is zero. The low reflectivity of the target is negated by increasing the intensity of the reference fields (non-entangled) in the homodyne. Based on heuristic arguments, a lower bound of the target's reflectivity for optimum application of this technique is described.

DOI
10.48550/arxiv.2310.18610

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The quantum illumination technique requires joint measurement between the idler and the probe reflected from the low-reflective target present in a noisy environment. The joint measurement is only possible with prior knowledge about the target's location. The technique in this article overcomes this limitation by using entanglement and a cross-correlated homodyne measurement. This technique does not require quantum storage of the idler and prior knowledge about the target's distance. The cross-correlation measurement makes this technique completely immune to environmental noise, as the correlation between the idler and the environment is zero. The low reflectivity of the target is negated by increasing the intensity of the reference fields (non-entangled) in the homodyne. Based on heuristic arguments, a lower bound of the target's reflectivity for optimum application of this technique is described.
Quantum illumination (QI) is implemented by a joint measurement between the idler field and the signal field reflected from the low-reflectivity stationary target in a noisy environment. The joint measurement is possible only with prior knowledge of the target's location, which is unknown in many cases. The technique described in this article overcomes this limitation by using optical entanglement and quantum cross-correlated homodyne measurement. This technique offers the following additional advantages in comparison with QI implementation through joint measurement: (1) quantum storage and prior knowledge about the target's distance are not required, (2) it adds ranging capability, and (3) it adds anti-stealth mechanism to suppress the low-reflectivity of the target. As the detection is at optical frequencies, the environment is considered as a stray laser, which could be a decoy, a jamming field, a probe field from another ranging application, or a field used to mask the actual probe. Thus, the environment considered in this Letter is suitable for ranging applications like lidar.
An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.
Quantum illumination (QI) promises unprecedented performances in target detection, but there are various problems surrounding its implementation. Where target ranging is a concern, signal and idler recombination forms a crucial barrier to the protocol's success. This could potentially be mitigated if performing a measurement on the idler mode could still yield a quantum advantage. In this article, we investigate the QI protocol for a generically correlated Gaussian source and study the phase-conjugating (PC) receiver, deriving the associated SNR in terms of the signal and idler energies, and their cross-correlations, which may be readily adapted to incorporate added noise due to Gaussian measurements. We confirm that a heterodyne measurement performed on the idler mode leads to a performance, which asymptotically approaches that of a coherent state with homodyne detection. However, if the signal mode is affected by heterodyne but the idler mode is maintained clean, the performance asymptotically approaches that of the PC receiver without any added noise.
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.
Quantum illumination exploits entanglement between a transmitted signal and a retained idler to improve the error-probability exponent of target detection by roughly a factor of four (6 dB) over that with a coherent state of the same transmitted energy. This advantage presumes a known return phase. In practice, the phase is set by the range to the target and the condition of its surface, and is difficult to know in advance. Whether the advantage survives when this phase is unknown is not obvious. Here, we cast target detection as a composite hypothesis test in which the return phase is an unknown constant common to all trials, and we restrict the receiver to independent and identical measurements on each copy. We bound the worst-case error exponent at low reflectivity for every such measurement and every input state of a single signal mode and an idler of any dimension. We then show that unentangled coherent light with heterodyne detection already saturates this bound, for every value of the phase. Entanglement therefore confers no advantage in this setting. The class of independent and identical measurements contains many implementable quantum-illumination receivers, including the optical parametric amplifier and phase-conjugate receivers. Our result shows that none of them can offer a quantum advantage in the worst case over the phase, to leading order in the reflectivity.
Quantum illumination is one of the main paradigms for implementing quantum radar in the low-frequency spectrum. Here, we discuss how to ease the open-air application of the protocol. I first define an experimentally feasible receiver for an entangled signal-idler transmitter. This consists of measuring heterodyne the received signal and adaptively measuring homodyne the idler, reaching a maximal quantum advantage of 3 dB in the error probability exponent with respect to the optimal classical strategy. Our receiver requires only a single tunable JPA. To relax the bandwidth requirement at the transmitter level, we discuss a sequential protocol that uses patches of modes sequentially to probe the target region. We show that, in a practical scenario, the sequential protocol needs two orders of magnitude less bandwidth with respect to the non-sequential protocol, while keeping the same quantum advantage. We finally briefly discuss possible applications of quantum illumination for backscatter communication and covert communication.