Sensing frequencies at the discrete Grover-Heisenberg limit using a single qubit

arXiv:2611.15057v1 Announce Type: new Abstract: We consider a fundamental quantum sensing task: detecting weak oscillating fields with unknown strength and frequency. Recent work by Allen et al. established a fundamental lower bound on the required sensing time, which they named the "Grover-Heisenberg limit", and gave a protocol attaining this limit. The protocol relies on auxiliary qubits, which are used to run Grover's algorithm as a subroutine, leaving open the question of whether a single sensing qubit can achieve the same scaling. We show that a single qubit suffices for a discrete version of this problem, in which the signal strength is known and the frequency belongs to an arbitrary, but known, finite set of candidate frequencies.