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.
Highlights
We find that the behavior of the Fisher information is somewhat more complicated than that presented in ref
We find that the behavior of the Fisher information in de Sitter (dS) and Anti-de Sitter (AdS) share similar phenomenology, at late times
We have studied the Fisher information for estimating the temperature experienced by detectors of various trajectories in dS and AdS spacetimes
Summary
The parameter estimation problem is concerned with how the value of a given physical quantity that is not directly observable can be inferred via its statistical effects on quantities that are observable. States that the mean-squared error of any unbiased estimator ξof ξ is lower bounded by the reciprocal of the Fisher information. Fisher information is the quantity that yields an ultimate bound on the precision attainable in a parameter estimation problem. Both dS4 and AdS4 can be represented as 4-dimensional hyperboloids embedded in 5dimensional spacetimes, ds2 = −dX02 + dX12 + dX22 + dX32 ± dX42,. The quantity = 3/Λ ≡ 1/k is referred to as the (A)dS length in both cases, the dS case (which takes the minus sign in eq (2.5)) having a coordinate singularity at the cosmological horizon r =. We study a massless real scalar field φ conformally coupled to curvature via the action
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