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

• Published in: The journal of high energy physics Vol. 2021; no. 5; pp. 1 - 22
• Main Authors: Du, Haoxing, Mann, Robert B.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2021; Springer Nature B.V; SpringerOpen
• Subjects: Boundary conditions; Classical and Quantum Gravitation; Effective Field Theories; Elementary Particles; Energy gap; Estimation; Expected values; Fisher information; Gravitational waves; High energy physics; Investigations; Metrology; Models of Quantum Gravity; Parameter estimation; Phenomenology; Physics; Physics and Astronomy; Quantum Dissipative Systems; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativistic effects; Relativity Theory; Scalars; Sensors; Spacetime; String Theory; Temperature dependence; Theory of relativity; Quantum Dissipative Systems; Effective Field Theories; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2021)112

A
bstract
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.