Parameter estimation for a Lorentz invariance violation

TL;DR

This paper uses quantum estimation theory to analyze how precisely Lorentz violation parameters can be estimated in flat spacetime, highlighting optimal conditions and the significance of Planck-scale effects.

Contribution

It introduces a quantum Fisher information framework for Lorentz violation parameter estimation and identifies conditions for maximum precision.

Findings

Maximum quantum Fisher information at specific momentum

Optimal estimation precision near the Planck scale

Explicit expression of QFI in terms of Lorentz violation parameters

Abstract

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 $k_{\mathrm{max}}$. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.