Quantum CramerRao Bound for a Massless Scalar Field in de Sitter Space
Abstract
How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of measurementdependent Fisher information and ultimately by quantum Fisher information, which is the maximization of the former over all positive operator valued measurements. Such bound is known as the quantum CramerRao bound. We consider the evolution of a massless scalar field with BunchDavies vacuum in a spatially flat FLRW spacetime, which results in a twomode squeezed vacuum outstate for each field wave number mode. We obtain the expressions of the quantum Fisher information as well as the Fisher informations associated to occupation number measurement and power spectrum measurement, and show the specific results of their evoluation for pure de Sitter expansion and de Sitter expansion followed by a radiationdominated phase as examples. We will discuss these results from the point of view of the quantumtoclassical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.
 Publication:

Universe
 Pub Date:
 October 2017
 DOI:
 10.3390/universe3040071
 arXiv:
 arXiv:1707.09702
 Bibcode:
 2017Univ....3...71R
 Keywords:

 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 16 pages, published version