Entanglement-enhanced quantum sensors for particle trajectory discrimination

The trajectory of a particle through space reveals some of its most important properties, such as its charge, energy, and lifetime. We introduce the following model for a quantum trajectory sensor: suppose an incident particle interacts with an array of qubits, imparting a spatial perturbation pattern which depends on its trajectory. If the initial sensor state is appropriately chosen, then the possible patterns might be distinguishable using a single projective measurement. However, it is nontrivial to efficiently find a suitable sensor state, since the system of constraints on the state is typically very large. To overcome this obstacle, we develop a group-theoretic framework which exponentially reduces the size of this system when the trajectories obey certain symmetries. These simplified sensor criteria yield general families of trajectory sensing (TS) states, and we prove that entanglement can dramatically reduce the particle-qubit interaction strength necessary to achieve perfect TS via a single measurement. Furthermore, we establish a rigorous correspondence between TS and quantum error correction, which both seek to identify perturbations using measurements. By virtue of this connection, a number of familiar stabilizer codes (e.g., toric codes) are in fact useful for TS.