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The European Physical Journal Plus

Quantum entanglement of two bosonic modes in de Sitter space

Madalin Calamanciuc, Аурелиан Исар

Published Sep 3, 2025• 0 citations
Publisher

Abstract

Abstract The time evolution of Gaussian quantum entanglement of two bosonic modes associated with a scalar quantum field in de Sitter space and in interaction with a thermal reservoir is investigated in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that quantum entanglement strongly depends on the squeezing of the bimodal state, the parameters characterizing the thermal environment, the curvature parameter of de Sitter space, and the mass parameter. The thermal environment and the curvature have a destructive influence on the entanglement, whose survival time depends on the competition between the contrary effects provided by the squeezing of the bimodal state, the curvature, and the thermal bath. The entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field, respectively, minimally coupled massless field.

DOI
10.1140/epjp/s13360-025-06768-1

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Abstract The time evolution of Gaussian quantum entanglement of two bosonic modes associated with a scalar quantum field in de Sitter space and in interaction with a thermal reservoir is investigated in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that quantum entanglement strongly depends on the squeezing of the bimodal state, the parameters characterizing the thermal environment, the curvature parameter of de Sitter space, and the mass parameter. The thermal environment and the curvature have a destructive influence on the entanglement, whose survival time depends on the competition between the contrary effects provided by the squeezing of the bimodal state, the curvature, and the thermal bath. The entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field, respectively, minimally coupled massless field.
We review the results obtained by investigating, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the time evolution of quantum entanglement of two different bimodal systems, each one interacting with a thermal environment. The first system is formed of the free massless bosonic mode of a stationary observer in a region that is asymptotically flat (Kruskal observer) or freely falling in Schwarzschild black hole, and the mode of a uniformly accelerated observer hovering outside the event horizon of black hole. For initial bimodal Gaussian squeezed thermal states of the system, we show that under the influence of Hawking radiation the quantum entanglement of the two modes is destroyed in a finite time, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. The second system consists of two bosonic modes associated with a scalar quantum field in de Sitter space, characterized by two regions that are causally disconnected and described using open universe coordinates on two open charts. The survival time of the entanglement of this bimodal system strongly depends on the competition between the contrary effects provided by the squeezing of the initial bimodal state, the curvature of de Sitter space, the mass parameter and the thermal environment. It is shown that the entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field and, respectively, minimally coupled massless field.
We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.
We describe the time evolution of the quantum coherence in an open system consisting of two coupled bosonic modes embedded in a thermal reservoir. We discuss the influence of the environment in terms of the covariance matrix for initial squeezed thermal states. The coherence is quantified using the relative entropy as a measure, and its dynamics is studied in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that the evolution of the quantum coherence strongly depends on the initial state of the system (squeezing parameter and thermal photon numbers), the parameters characterizing the thermal reservoir (temperature and dissipation coefficient) and the intensity of the coupling between the two modes.
The Hilbert-Schmidt measure is a useful geometric tool used to investigate the properties on the manifold of mixed Gaussian states in multimode continuous variable quantum systems. In this work, we study the relationship between the scalar curvature and quantum entanglement across causally disconnected regions (open charts) in de Sitter spacetime. We first consider a two-mode squeezed state shared between Alice and Bob, where the Gaussian channel models the effects of spacetime curvature. We employ logarithmic negativity as a witness for quantum entanglement. We study the impact of the mass, parameter p and squeezing parameter on the scalar curvature and entanglement. We find an interesting interplay between scalar curvature and entanglement for certain values of the mass and parameter p . By varying p , we thus explore how information geometry and entanglement are influenced by both ultraviolet and infrared modes. Moreover, the relationship between scalar curvature and entanglement is discussed under the influence of various parameters characterizing the geometric system under consideration.
We study the evolution of the entanglement of two independent bosonic modes embedded in a thermal environment, in the framework of the theory of open quantum systems. As a measure of entanglement we use the logarithmic negativity. For a non-zero temperature of the thermal reservoir the entangled initial Gaussian states become always separable in a finite time. For initial squeezed thermal states we calculate the survival time of entanglement and analyze its dependence on temperature, squeezing parameter and mean thermal photon numbers. For a zero temperature of the thermal bath an entangled initial state remains entangled for all finite times, but in the limit of asymptotically large times it becomes separable.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of continuous variable quantum entanglement and quantum discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that discord decays asymptotically in time under the effect of the thermal bath. We describe also the time evolution of classical correlations.