Relativistic motion enhanced quantum estimation of $$\kappa $$ κ -deformation of spacetime

Abstract We probe the $$\kappa $$ κ -deformation of spacetime using a two-level atom as a detector coupled to a $$\kappa $$ κ -deformed massless scalar field which is invariant under a $$\kappa $$ κ -Poincaré algebra and written in commutative spacetime. To address the quantum bound to the estimability of the deformation parameter $$\kappa $$ κ , we perform measurements on the two-level detector and maximize the value of quantum Fisher information over all possible detector preparations. We prove that the population measurement is the optimal measurement in the estimation of the deformation parameter $$\kappa $$ κ . In particular, we show that the relativistic motion of the detector affects the precision in the estimation of the parameter $$\kappa $$ κ , which can effectively improve this precision comparing to that of the static detector case by many orders of magnitude.