Quantum entanglement enables single-shot trajectory sensing for weakly interacting particles

Sensors for mapping the trajectory of an incoming particle find important utility in experimental high energy physics and searches for dark matter. For a quantum sensing protocol that uses projective measurements on a multi-qubit sensor array to infer the trajectory of an incident particle, we establish that entanglement can dramatically reduce the particle-qubit interaction strength $\theta$ required for perfect trajectory discrimination. Within an interval of $\theta$ above this reduced threshold, any unentangled sensor requires $\Theta(\log(1/\epsilon))$ repetitions of the protocol to estimate a previously unknown particle trajectory with $\epsilon$ error probability, whereas an entangled sensor can succeed with zero error in a single shot. Furthermore, entanglement can enhance trajectory sensing in realistic scenarios where $\theta$ varies continuously over the sensor qubits, exemplified by a Gaussian-profile laser pulse propagating through an array of atoms.