One-shot discrimination of weak digital time-domain signals with entangled quantum sensors

The discrimination of digital time-domain signals is an essential component of numerous diverse technologies, such as communication networks and sensors for particle physics and neuroscience. We introduce the following quantum model for this discrimination scenario: a qubit array is exposed to an unknown discrete-time binary signal such that each qubit is rotated by a fixed angle $\alpha$ during every time step where the signal has value 1. The goal is to determine an appropriate initial state and to apply suitable control unitaries at each step so that a single, final projective measurement unambiguously identifies the signal from a known set of candidates. We derive criteria which relate the one-shot distinguishability of a signal set to parameters such as the number of candidates, the signal strength $\alpha$, and the number of qubits. Furthermore, we find that entangled sensors can achieve one-shot discrimination even when $\alpha$ is too weak for an unentangled sensor to perfectly succeed. Our solutions employ tools from quantum signal processing to transduce the time-domain signals into spatially-patterned perturbations over the array; the latter can then be identified using special sensor states closely related to those previously developed for particle trajectory sensing.