We study the distribution of bipartite and tripartite 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 Gaussian Rényi-2 entanglement as a witness for quantum entanglement, while Gaussian geometric discord is a measure of quantumness beyond entanglement, including entanglement. The Gaussian Rényi-2 classical correlations are used to quantify the correlations. Besides, we achieve tripartite entanglement among the open chart modes, quantified by residual Gaussian Rényi-2 entanglement. Our results demonstrate the generation of bipartite entanglement between spatially separated observers due to strong curvature. The impact of curvature on both classical and quantum correlations is shown to be particularly pronounced for conformal and massless scalar fields. Hence, residual Gaussian Rényi-2 entanglement is generated among the open chart modes due to the influence of de Sitter curvature for all nonzero squeezing values.
We study the distribution of bipartite and tripartite 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 Gaussian Rényi-2 entanglement as a witness for quantum entanglement, while Gaussian geometric discord is a measure of quantumness beyond entanglement, including entanglement. The Gaussian Rényi-2 classical correlations are used to quantify the correlations. Besides, we achieve tripartite entanglement among the open chart modes, quantified by residual Gaussian Rényi-2 entanglement. Our results demonstrate the generation of bipartite entanglement between spatially separated observers due to strong curvature. The impact of curvature on both classical and quantum correlations is shown to be particularly pronounced for conformal and massless scalar fields. Hence, residual Gaussian Rényi-2 entanglement is generated among the open chart modes due to the influence of de Sitter curvature for all nonzero squeezing values.
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.
In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.
Studies of quantum field entanglement in de Sitter space based on the von Neumann entropy of local patches have concluded that curvature enhances entanglement between regions and their complements. Similar conclusions about entanglement enhancement have been reached in analyses of Fourier modes in the cosmological patch of de Sitter space. We challenge this interpretation by adopting a fully local approach: examining entanglement between pairs of field modes compactly supported within de Sitter's cosmological patch. Our approach is formulated in terms of the properties of a metric tensor and an associated complex structure induced by the Bunch-Davies vacuum on the classical phase space. We find that increasing curvature increases correlations between local modes but, somewhat counterintuitively, decreases their entanglement. Our methods allow us to characterize how entanglement is spatially distributed, revealing that a cosmological constant, even if tiny, qualitatively alters the vacuum's entanglement structure. We show that our results are compatible with previous entropy-based studies when properly interpreted. Our findings have implications for entanglement between observables generated during cosmic inflation.
We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice.
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.
Here, we study quantum coherence of N-partite GHZ (Greenberger-Horne-Zeilinger) and W states in the multiverse consisting of N causally disconnected de Sitter spaces. Interestingly, N-partite coherence increases monotonically as the curvature increases, while the Unruh effect destroys multipartite coherence in Rindler spacetime. Conversely, the curvature effect destroys quantum entanglement and discord, meaning that the curvature effect is beneficial to quantum coherence and harmful to quantum correlations in the multiverse. We find that, with the increase of n expanding de Sitter spaces, N-partite coherence of GHZ state increases monotonically for any curvature, while quantum coherence of the W state decreases or increases monotonically depending on the curvature. We find a distribution relationship, which indicates that the correlated coherence of N-partite W state is equal to the sum of all bipartite correlated coherence in the multiverse. Multipartite coherence exhibits unique properties in the multiverse, which argues that it may provide some evidence for the existence of the multiverse.