Fisher information as a probe of spacetime structure: Relativistic quantum metrology in (A)dS

TL;DR

This paper explores how relativistic quantum effects influence temperature measurement precision in (A)dS spacetimes using quantum detectors, revealing factors that optimize estimation accuracy.

Contribution

It introduces a unified analysis of Fisher information for temperature estimation in (A)dS spaces, considering acceleration, boundary conditions, and detector parameters.

Findings

Fisher information depends on temperature, curvature, and detector settings.

Unification of Fisher information phenomenology in dS and AdS.

Strategies identified to maximize temperature estimation precision.

Abstract

Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in (3+1)-dimensional de Sitter and anti-de Sitter space. Using Unruh-DeWitt detectors coupled to a massless scalar field as probes and treating them as open quantum systems, we compute the Fisher information for estimating temperature. We investigate the effect of acceleration in dS, and the effect of boundary condition in AdS. We find that the phenomenology of the Fisher information in the two spacetimes can be unified, and analyze its dependence on temperature, detector energy gap, curvature, interaction time, and detector initial state. We then identify estimation strategies that maximize the Fisher information and therefore the precision of estimation.