Abstract
In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure 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 alongwith 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, Re'nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.
Highlights
The theory of closed quantum systems is a very popular topic and has already been firmly established
The knowledge of complete time evolutionary dynamics of a quantum mechanical system requires incorporation of the details of the thermal environment, which paves the way towards the study of Open Quantum System [1,43,44,45,46] (OQS), where the physical system weakly interacts with the environment
In this work, we have addressed the following issues to study the quantum entanglement phenomenon from two entangled atomic OQS set up:
Summary
The theory of closed quantum systems is a very popular topic and has already been firmly established. We have taken into account the contributions from both the prime components of the master equation, the effective Lamb Shift Hamiltonian and the Lindbladian operator, which provides a complete solution of the master equation and gives us a proper understanding about the complete time evolution of the reduced density matrix of the two atomic subsystem Further using this result we have computed a number of information theoretic measures to quantify the quantum entanglement and study the entanglement dynamics and its dependence on various parameters of the system and background spacetime. 6, we explicitly calculate the analytical solution of the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation [19,20] for the case of two entangled atoms which mimics the role of Unruh-De-Witt detectors, which are minimally coupled to a probe massless scalar field placed in the thermal bath. We are primarily concerned about the two atomic system, by doing the following approximations we bring this non-Markovian integro-differential equation into a Gorini– Kossakowski–Sudarshan–Lindblad (GKSL) [19,20] master equation which is Markovian in nature and can be solved
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