Achieving the Quantum Limits with Twin-Field Sensors

Continuous measurements play a fundamental role in quantum experiments, yet understanding and extracting the maximal possible information in a continuous probe signal remains a significant challenge. In this work, we show that for a wide class of sensors, the quantum Fisher information bound can be saturated through a combined measurement of signals from the original sensor and a suitable system copy. We elucidate the physical mechanism of such a twin-field sensor (TFS) and study its performance across diverse implementations, ranging from two-level atoms to a hybrid quantum Rabi model. In all of these cases, we find that simple photon counting or homodyne detection saturates the theoretical quantum limit. We further prove that the TFS achieves the quantum limits for the joint sensing of pairs of parameters as quantified by the quantum Fisher information matrix.