Some measures for fermionic entanglement in the cosmological de sitter spacetime

Abstract

We investigate two measures of quantum correlations and entanglement, namely the violation of the BellMermin-Klyshko (BMK) inequalities and the quantum discord, for Dirac fermions in the cosmological de Sitter background of dimension four. The BMK violation is focussed on the vacuum for two and four mode squeezed states and the maximum violation is demonstrated. For the quantum discord, we investigate a maximally entangled in-vacuum state. Qualitative similarities as well as differences of our results with that of different coordinatisations of de Sitter in the context of scalar and fermionic field theory is discussed.