Statistical Bounds on CMB Bell Violation

TL;DR

This paper investigates the statistical variance in observing Bell's inequality violations in the cosmic microwave background, finding that for highly squeezed states like the CMB, the variance vanishes, reducing uncertainties.

Contribution

It provides a theoretical analysis showing that for highly squeezed primordial states, the statistical variance in Bell violation measurements is negligible.

Findings

Statistical variance vanishes for highly squeezed states

Variance depends on the choice of pseudo-spin operators

Reduces uncertainties in CMB Bell violation observations

Abstract

Inspired the low $\ell$ cosmic variance we present a study on the statistical variance expected in observing Bell's inequality violation by primordial quantum states violation. We consider the statistical variance inherent to three sets of pseudo-spin operators used to construct Bell's inequality. We find that for a highly squeezed state, such as the relevant CMB states, the statistical variation will vanish and does not contribute to theoretical uncertainties.