A theoretical work establishes the ultimate sensitivity limits for measuring small transverse beam displacements and proposes strategies that attain them, within the framework of mode parameter estimation. The authors compare two families of states with different resource constraints, built from Hermite-Gauss and Laguerre-Gauss mode pairs, and analyse which one offers the best possible spatial resolution for given quantum resources.

For states with fixed total photon number, the optimal state turns out to be, asymptotically, a rotated NOON state. This result is contrasted with that of an asymptotically optimal pure Gaussian state under the constraint of fixed average photon number, allowing a comparison between two common notions of "resource" in quantum metrology and showing how the sensitivity bound changes depending on which one is imposed.

On the experimental side, the authors propose concrete measurement schemes based on the method of moments. In particular, they point out that the twin-Fock state may provide a viable alternative to the rotated NOON state for this task, with the practical advantage of being more accessible in the laboratory.

The work thus provides a broader benchmark for developing practical strategies for spatial sensing at the quantum limit, with implications for beam displacement sensors, high-precision optical alignment and position-sensitive microscopy.