Does relativistic motion always degrade quantum Fisher information?

TL;DR

This paper examines how relativistic motion affects the quantum Fisher information of a two-level atom detector, revealing conditions under which relativistic effects can either degrade or preserve quantum estimation precision.

Contribution

It uncovers the nuanced influence of combined linear acceleration and velocity on quantum Fisher information, highlighting scenarios where relativistic motion can enhance quantum parameter estimation.

Findings

Inertial motion does not affect quantum Fisher information but causes decay over time.

Linear acceleration reduces quantum Fisher information in state estimation.

High velocities can shield quantum Fisher information from environmental effects.

Abstract

We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ($w=0$) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\tau$, we find quite unlike the previous results that, for the non-relativistic case $(w\ll1)$, the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultra-relativistic velocities $(w\rightarrow\infty)$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shield from the effect of the external environment, and thus from the relativistic motion.