Joint optimization of squeezing and coherent displacement

Determine the jointly optimal squeezing spectrum and coherent displacement for passive Gaussian metrology under a fixed total photon-number budget.

Background

The paper shows that coherent displacement can lift a covariance-wall degeneracy when the corresponding passive generator acts nontrivially on the first moments. Displacement energy, however, consumes part of the same total photon-number resource used for squeezing, creating a resource-allocation problem between covariance-based sensitivity and first-moment sensitivity. The authors explicitly identify the joint optimization of these resources as unresolved.