  Detecting if and when objects change is difficult in passive sub-diffraction
imaging of dynamic scenes. We consider the best possible tradeoff between
responsivity and accuracy for detecting a change from one arbitrary object
model to another in the context of sub-diffraction incoherent imaging. We
analytically evaluate the best possible average latency, for a fixed false
alarm rate, optimizing over all physically allowed measurements of the optical
field collected by a finite 2D aperture. We find that direct focal-plane
detection of the incident optical intensity achieves sub-optimal detection
latencies compared to the best possible average latency, but that a three-mode
spatial-mode demultiplexing measurement in concert with on-line statistical
processing using the well-known CUSUM algorithm achieves this quantum limit for
sub-diffraction objects. We verify these results via Monte Carlo simulation of
the change detection procedure and quantify a growing gap between the
conventional and quantum-optimal receivers as the objects are more and more
diffraction-limited.
