Open Quantum Entanglement: A study of two atomic system in static patch of de Sitter space

TL;DR

This paper investigates quantum entanglement and non-locality between two atoms in the static patch of de Sitter space, using information-theoretic measures and a master equation approach to understand long-range quantum effects in a cosmological setting.

Contribution

It develops an analytical framework for studying two-atom entanglement in de Sitter space, incorporating a thermal bath and deriving explicit entanglement measures and Bell inequality violations.

Findings

Entanglement persists over long distances in de Sitter space.

Various entanglement measures indicate significant quantum correlations.

Bell-CHSH inequality is violated, confirming non-locality.

Abstract

In this work, our prime objective is to study non-locality and long-range effects of two-body correlation using quantum entanglement from the various information-theoretic measures in the static patch of de Sitter space using a two-body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result along with the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$e'$nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystems on the static patch of De-Sitter space. Finally, we have studied the violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.