  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, 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.
