Quantum Fisher information for general spatial deformations of quantum emitters

Understand

We present a framework for the detection and estimation of deformations applied to a grid of sources.

• Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify the amount of information we have on the deformation matrix.
• Quantum metrology for grid deformations provides an ideal testbed to examine multi-parameter estimations for arbitrarily parameterised channel evolutions with generally non-commuting Hermitian generators.
• We generalise the local generator of translations for deformation parameters to multi-parameter estimations and use it to explore how well different deformations can be detected and corrected for.