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We introduce spatial deformations to an array of light sources and study howthe estimation precision of the interspacing distance, d, changes with thesources of light used. The quantum Fisher information (QFI) is used as thefigure of merit in this work to quantify the amount of information we have onthe estimation parameter. We derive the generator of translations, G, in d dueto an arbitrary homogeneous deformation applied to the array. We show how thevariance of the generator can be used to easily consider how differentdeformations and light sources can effect the estimation precision. The singleparameter estimation problem is applied to the array and we report on theoptimal state that maximises the QFI for d. Contrary to what may have beenexpected, the higher average mode occupancies of the classical states performsbetter in estimating d when compared with single photon emitters (SPEs). Theoptimal entangled state is constructed from the eigenvectors of the generatorand found to outperform all these states. We also find the existence ofmultiple optimal estimators for the measurement of d. Our results findapplications in evaluating stresses and strains, fracture prevention inmaterials expressing great sensitivities to deformations, and selectingfrequency distinguished quantum sources from an array of reference sources.

Quantum metrology of spatial deformation using arrays of classical and quantum light emitters