The temporal resolution limit in quantum sensing

Temporal resolution is a critical figure of merit in quantum sensing. This study combines the distinguishable condition of quantum states with quantum speed limits to establish a lower bound on interrogation time. When the interrogation time falls below this bound, the output state becomes statistically indistinguishable from the input state, and the information will inevitably be lost in noise. Without loss of generality, we extend these conclusions to time-dependent signal Hamiltonian. In theory, leveraging certain quantum control techniques allows us to calculate the minimum interrogation time for arbitrary signal Hamiltonian. Finally, we illustrate the impact of quantum speed limits on magnetic field measurements and temporal resolution.