Parameter estimation for a Lorentz invariance violation

We employ techniques from quantum estimation theory (QET) to estimate the Lorentz violation parameters in the 1+3-dimensional flat spacetime. We obtain and discuss the expression of the quantum Fisher information (QFI) in terms of the Lorentz violation parameter ${\sigma }_0$ and the momentum k of the created particles. We show that the maximum QFI is achieved for a specific momentum $k_{\mathrm{m}\mathrm{a}\mathrm{x}}$. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.