Improved Sensing with a Single Qubit

We consider quantum metrology with arbitrary prior knowledge of the parameter. We demonstrate that a single sensing two-level system can act as a virtual multilevel system that offers increased sensitivity in a Bayesian single-shot metrology scenario, and that allows one to estimate (arbitrary) large parameter values by avoiding phase wraps. This is achieved by making use of additional degrees of freedom or auxiliary systems not participating in the sensing process. The joint system is manipulated by intermediate control operations in such a way that an effective Hamiltonian, with an arbitrary spectrum, is generated that mimics the spectrum of a multisystem interacting with the field. We show how to use additional internal degrees of freedom of a single trapped ion to achieve a high-sensitivity magnetic field sensor for fields with arbitrary prior knowledge.

Figure 1

Optimal variance attained by an equally gapped $n$-level state for $2\le n\le 9$. The dots correspond to the times where the controls are turned on to either measure out the state or prepare the optimal state for the next time. Inset: Optimal states for each time step. The ordinate depicts the total phase acquired by each level at a given time, and the area of each circle corresponds to the weight of each level for the optimal states.