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.
Highlights
Quantum entanglement is a highly counterintuitive feature of quantum mechanics related to its nonlocal characteristics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
The subject has been put on a firm physical ground since its first experimental verification [5,6] and in recent times it has developed various disciplines involving the quantum information and computation, see [20] and references therein
The most well studied case of quantum entanglement in this context corresponds to the Rindler left-right wedges [21,22,23,24,25,26,27,28,29,30,31]
Summary
Quantum entanglement is a highly counterintuitive feature of quantum mechanics related to its nonlocal characteristics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Our study on the BMK violation will be focused on the vacuum, whereas for the quantum discord we shall work on some maximally entangled initial Bell state, which will give us insight about correlations between nonvacuum states. In [42], the infinite BMK violation was demonstrated for a massless scalar field in a cosmological background which is de Sitter and radiation dominated respectively in the past and future We shall compute these two measures for massive Dirac fermions in the cosmological de Sitter background in order to see how much similar or dissimilar the result is with the already existing results. We work in spacetime dimension four and set c 1⁄4 1 1⁄4 ħ
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