Quantum estimation of a charge distance from a hole-spin qubit in Si quantum dots

Hole-spin qubits in semiconductors represent a mature platform for quantum technological applications. Here we consider their use as sensors of the electrostatic environment, and specifically for estimating the distance from the qubit of an external charge. Different approaches are considered -- based on the use of single or double quantum dots, ground and out-of-equilibrium states, Rabi and Ramsey measurements -- and comparatively analyzed by means of the classical and quantum Fisher information. Detailed quantitative aspects result from the multiband character of the hole states, which we account for within a multiband approach. Beyond this, general conclusions can be drawn on the relative efficiency of the above options, and analytical expressions are derived for the Fisher information of a generic qubit within the Rabi and Ramsey schemes.