Some measures for fermionic entanglement in the cosmological de Sitter spacetime

TL;DR

This paper examines quantum correlations and entanglement measures, specifically Bell inequality violations and quantum discord, for Dirac fermions in four-dimensional de Sitter spacetime, revealing mode-dependent behaviors and comparing different coordinate systems.

Contribution

It provides the first detailed analysis of fermionic entanglement measures in de Sitter space, highlighting how these measures vary with mode number and coordinate choices.

Findings

Bell-Mermin-Klyshko violation increases with the number of modes.

Quantum discord shows qualitative similarities and differences across coordinate systems.

Entanglement measures depend on the state and mode structure in de Sitter spacetime.

Abstract

We investigate two measures of quantum correlations and entanglement, namely the violation of the Bell-Mermin-Klyshko 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 it is shown to increase with the number of modes. 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.