Single Photon Quantum Ranging: When Sequential Decoding Meets High Dimensional Entanglement

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.