We present a new method for target finding and ranging in Lidar applications using high-dimensional Bell states. Combined with a sequential decision rule, this scheme asymptotically achieves zero error probability with finite energy expenditure. This result stems from the synergy of high-dimensional entanglement suppressing false positives and the sequential decision rule optimizing energy usage. It effectively provides a pathway to unbounded quantum advantage over classical methods and has substantial implications for high-precision sensing in noisy environments.
Abstract 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.
Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this paper, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol to test the entanglement of the target state in the lab. Using the
3-setting protocols generated by our method, we experimentally certify
2- and
3-dimensional entanglement in
4-dimensional unfaithful states.