  We consider the quantum ranging problem in the low noise level per mode and
low reflectivity (high loss) regime. We focus on single photon transmission
strategies and propose a novel approach that combines high dimensional time-bin
entanglement at the transmitter with a carefully constructed sequential
decision rule at the detector. Our analytical results establish the significant
performance gains that can be leveraged from this approach in a range of
operating parameters, as compared to the single photon classical approach, the
two-mode squeezed vacuum ranging scheme proposed earlier, and even the
block-based classical scheme. One can attribute this performance gain to 1) the
ability of the high dimensional time-bin entangled signaling to offer a very
fine range resolution with a single transmitted photon and 2) the ability of
the sequential decision rule to minimize the average number of transmitted
photon subject to a constraint on the probability of error. While our analysis
is limited to the low energy/low noise regime, we conjecture that the proposed
approach's superior performance extends to a wider range of scenarios which
should motivate further analytical and experimental investigations.
