  Accurate time-delay measurement is at the core of many modern technologies.
Here, we present a temporal-mode demultiplexing scheme that achieves the
ultimate quantum precision for the simultaneous estimation of the temporal
centroid, the time offset, and the relative intensities of an incoherent
mixture of ultrashort pulses at the single-photon level. We experimentally
resolve temporal separations ten times smaller than the pulse duration, as well
as imbalanced intensities differing by a factor of $10^{2}$. This represents an
improvement of more than an order of magnitude over the best standard methods
based on intensity detection.
