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Phase-Conjugate Receiver for Gaussian-State Quantum Illumination

Baris I. Erkmen, Saikat Guha

Published Aug 1, 2010• 0 citations
OpenAlex

Abstract

An active optical sensor probes a region of free space that is engulfed in bright thermal noise to determine the presence (or absence) of a weakly reflecting target. The returned light (which is just thermal noise if no target is present, and thermal noise plus a weak reflection of the probe beam if a target is present) is measured and processed by a receiver and a decision is made on whether a target is present. It has been shown that generating an entangled pair of photons (which is a highly nonclassical state of light), using one photon as the probe beam and storing the other photon for comparison to the returned light, has superior performance to the traditional classical-light (coherent-state) target detection sensors. An entangled-photon transmitter and optimal receiver combination can yield up to a factor of 4 (i.e., 6 dB) gain in the error-probability exponent over a coherent state transmitter and optimal receiver combination, in a highly lossy and noisy scenario (when both sensors have the same number of transmitted photons). However, the receiver that achieves this advantage is not known. One structured receiver can close half of the 6-dB gap (i.e., a 3-dB improvement). It is based on phase-conjugating the returned light, then performing dual-balanced difference detection with the stored half of the entangled-photon pair. Active optical sensors are of tremendous value to NASA s missions. Although this work focuses on target detection, it can be extended to imaging (2D, 3D, hyperspectral, etc.) scenarios as well, where the image quality can be better than that offered by traditional active sensors. Although the current work is theoretical, NASA s future missions could benefit significantly from developing and demonstrating this capability. This is an optical receiver design whose components are, in principle, all implementable. However, the work is currently entirely theoretical. It is necessary to: 1. Demonstrate a bench-top proof of the theoretical principle, 2. Create an operational prototype off-the-bench, and 3. Build a practical sensor that can fly in a mission.

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An active optical sensor probes a region of free space that is engulfed in bright thermal noise to determine the presence (or absence) of a weakly reflecting target. The returned light (which is just thermal noise if no target is present, and thermal noise plus a weak reflection of the probe beam if a target is present) is measured and processed by a receiver and a decision is made on whether a target is present. It has been shown that generating an entangled pair of photons (which is a highly nonclassical state of light), using one photon as the probe beam and storing the other photon for comparison to the returned light, has superior performance to the traditional classical-light (coherent-state) target detection sensors. An entangled-photon transmitter and optimal receiver combination can yield up to a factor of 4 (i.e., 6 dB) gain in the error-probability exponent over a coherent state transmitter and optimal receiver combination, in a highly lossy and noisy scenario (when both sensors have the same number of transmitted photons). However, the receiver that achieves this advantage is not known. One structured receiver can close half of the 6-dB gap (i.e., a 3-dB improvement). It is based on phase-conjugating the returned light, then performing dual-balanced difference detection with the stored half of the entangled-photon pair. Active optical sensors are of tremendous value to NASA s missions. Although this work focuses on target detection, it can be extended to imaging (2D, 3D, hyperspectral, etc.) scenarios as well, where the image quality can be better than that offered by traditional active sensors. Although the current work is theoretical, NASA s future missions could benefit significantly from developing and demonstrating this capability. This is an optical receiver design whose components are, in principle, all implementable. However, the work is currently entirely theoretical. It is necessary to: 1. Demonstrate a bench-top proof of the theoretical principle, 2. Create an operational prototype off-the-bench, and 3. Build a practical sensor that can fly in a mission.
The signal half of an entangled twin beam, generated using spontaneous parametric downconversion, interrogates a region of space that is suspected of containing a target and has high loss and high (entanglement-breaking) background noise. A joint measurement is performed on the returned light and the idler beam that was retained at the transmitter. An optimal quantum receiver, whose implementation is not yet known, was shown to achieve 6 dB gain in the error-probability exponent relative to that achieved with a single coherent-state (classical) laser transmitter and the optimum receiver. We present two structured optical receivers that achieve up to 3 dB gain in the error exponent over that attained with the classical sensor. These are designs of quantum-optical sensors for target detection, which can be readily implemented in a proof-of-concept experiment, that appreciably outperform the best classical sensor in the low-signal-brightness, high-loss, and high-noise operating regime.
An optical transmitter that uses entangled light generated by spontaneous parametric downconversion (SPDC), in conjunction with an optimal quantum-optical receiver (whose implementation is not yet known) is in principle capable of obtaining up to a 6 dB gain in the error-probability exponent over the optimum-reception un-entangled coherent-state lidar to detect the presence of a far-away target subject to entanglement-breaking loss and noise in the free-space link . We present an explicit design of a structured quantum-illumination receiver, which in conjunction with the SPDC transmitter is shown to achieve up to a 3 dB error-exponent advantage over the classical sensor. Apart from being fairly feasible for a proof-of-principle demonstration, this is to our knowledge the first structured design of a quantum-optical sensor for target detection that outperforms the comparable best classical lidar sensor appreciably in a low-brightness, lossy and noisy operating regime.
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.
Abstract. Loss and noise quickly destroy quantum entanglement. Nevertheless, recent work has shown that a quadrature-entangled light source can reap a substantial performance advantage over all classical-state sources of the same average transmitter power in scenarios whose loss and noise makes them entanglement breaking [1, 2, 3, 4, 5, 6], standoff target-detection being an example. In this paper, we make a first step in extending this quantum illumination paradigm to the optical imaging domain, viz., to obtain better spatial resolution for standoff optical sensing. Our canonical imaging scenario—restricted, for simplicity, to one transverse dimension—is taken to be that of resolving one versus two closely-spaced in-phase specular point targets. We show that an entangled-state transmitter, which uses continuous-wave-pumped spontaneous parametric downconversion (SPDC), achieves an error-probability exponent that exceeds that of all classical-state transmitters of the same average power. Using these error-exponent results, we find the ultimate spatial-resolution limits for coherent-state and SPDC imaging systems that use their respective quantum-optimal receivers, thus quantifying the latter’s spatial-resolution advantage over the former. We also propose a structured optical receiver that is ideally capable of harnessing 3 dB (of the full 6 dB) gain in the error-probability exponent achievable by the SPDC transmitter and its quantum-optimal receiver.
In quantum illumination, the signal mode of light, entangled with an idler mode, is dispatched towards a suspected object bathed in thermal noise and the returning mode, along with the stored idler mode, is measured to determine the presence or absence of the object. In this process, entanglement is destroyed but its benefits in the form of classical correlations and enlarged Hilbert space survive. Here, we propose the use of probe state hyperentangled in two degrees of freedom - polarization and frequency, to achieve a significant 12dB performance improvement in error probability exponent over the best known quantum illumination procedure in the low noise regime. We present a simple receiver model using four optical parametric amplifiers (OPA) that exploits hyperentanglement in the probe state to match the performance of the feed-forward sum-frequency generator (FF-SFG) receiver in the high noise regime. By replacing each OPA in the proposed model with a FF-SFG receiver, further 3dB improvement in the performance of a lone FF-SFG receiver can be seen.
Quantum Lidar is a future technology that can mean different things to different people. To some it means detection and identification of classical-type lidar signals reflected from an illuminated target at or near the single photon level. This is facilitated by advances in semiconductor detector technology that allow highly efficient photocounting. To others it is more stringent, requiring exploitation of covertness associated with being essentially undetectable by the target in a thermal background, whilst allowing the lidar operator to filter her own signal from this noise. Again there is nothing specifically quantum about this. Any source that mimics of the energy rate per bandwidth seen by the illuminated object in the direction of the source can appear covert. In order to exploit quantum optics one can use inherent correlations, whether entangled or otherwise between light beams. Simple correlated optical beams can do this in two ways, perhaps by storing one beam as a reference and later performing correlated detection with the return signal in a phase sensitive manner. This is the “gold standard” for quantum lidar, but will be difficult outside of laboratory situations. In microscopy such phase control might be possible, or perhaps in the radio or microwave region for a quantum radar. Less challenging is a scenario in which an immediate local measurement of one beam conditions the beam sent to the target, allowing the return signal to be sifted from noise more easily. Here we will consider such a simple system, providing a range equation for a basic quantum lidar if it is to be operated covertly or openly. Open operation allows increased quantum signal brightness but also provides a quantum advantage, unspoofability – the lidar operator can in principle recognise their own return signal. We will also provide an analysis of quantum lidar detection based on quantum hypothesis testing and use this to perform Monte Carlo simulation of both target detections and false positive avoidance in a noisy background. The theory will be applied to experimental data.