TY - JOUR

T1 - Quantum cramer-Rao bound for a massless scalar field in de Sitter space

AU - Rotondo, Marcello

AU - Nambu, Yasusada

N1 - Funding Information:
Acknowledgments: Y.N. was supported in part by JSPS KAKENHI Grant Number 16H01094. M.R. gratefully acknowledges support from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
Publisher Copyright:
© 2017 by the authors.

PY - 2017/12

Y1 - 2017/12

N2 - 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 measurement-dependent 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 Cramer -Rao bound. We consider the evolution of a massless scalar field with Bunch-Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state 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 evolution for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.

AB - 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 measurement-dependent 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 Cramer -Rao bound. We consider the evolution of a massless scalar field with Bunch-Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state 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 evolution for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.

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U2 - 10.3390/universe3040071

DO - 10.3390/universe3040071

M3 - Article

AN - SCOPUS:85054481088

SN - 2218-1997

VL - 3

JO - Universe

JF - Universe

IS - 4

M1 - 71

ER -