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arXiv:1012.2548 · AIP conference proceedings

Enhanced standoff sensing resolution using quantum illumination

Saikat Guha, Jeffrey H. Shapiro, Timothy C. Ralph, Ping Koy Lam

Published Jan 1, 2011• 3 citations
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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.

DOI
10.1063/1.3630159

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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.
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.
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.
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.
Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon'quantum illumination' system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.
Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon'quantum illumination' system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.
Quantum illumination (QI) is an entanglement-enhanced sensing system whose performance advantage over a comparable classical system survives its usage in an entanglement-breaking scenario plagued by loss and noise. In particular, QI's error-probability exponent for discriminating between equally likely hypotheses of target absence or presence is 6 dB higher than that of the optimum classical system using the same transmitted power. This performance advantage, however, presumes that the target return, when present, has known amplitude and phase, a situation that seldom occurs in light detection and ranging (lidar) applications. At lidar wavelengths, most target surfaces are sufficiently rough that their returns are speckled, i.e., they have Rayleigh-distributed amplitudes and uniformly distributed phases. QI's optical parametric amplifier receiver---which affords a 3 dB better-than-classical error-probability exponent for a return with known amplitude and phase---fails to offer any performance gain for Rayleigh-fading targets. We show that the sum-frequency generation receiver [Zhuang et al., Phys. Rev. Lett. 118, 040801 (2017)]---whose error-probability exponent for a nonfading target achieves QI's full 6 dB advantage over optimum classical operation---outperforms the classical system for Rayleigh-fading targets. In this case, QI's advantage is subexponential: its error probability is lower than the classical system's by a factor of $1/ln(M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B})$, when $M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B}\ensuremath{\gg}1$, with $M\ensuremath{\gg}1$ being the QI transmitter's time-bandwidth product, ${N}_{S}\ensuremath{\ll}1$ its brightness, $\overline{\ensuremath{\kappa}}$ the target return's average intensity, and NB{N}_{B}NB​ the background light's brightness.