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Register a new userQuantum steering for continuous variable in de Sitter space
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We study the distribution of quantum steerability for continuous variables between two causally disconnected open charts in de Sitter space. It is shown that quantum steerability suffers from sudden death in de Sitter space, which is quite different from the behaviors of entanglement and discord because the latter always survives and the former vanishes only in the limit of infinite curvature. In addition, we find that the attainment of maximal steerability asymmetry indicates a transition between unidirectional steerable and bidirectional steerable. Unlike in the flat space, the asymmetry of quantum steerability can be completely destroyed in the limit of infinite curvature for the conformal and massless scalar fields in de Sitter space.
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We study the distribution of quantum entanglement for continuous variables among causally disconnected open charts in de Sitter space. It is found that genuine tripartite entanglement is generated among the open chart modes under the influence of curvature of de Sitter space for any nonzero squeezing. Bipartite entanglement is also generated when the curvature is strong enough, even though the observers are separated by the event horizon. This provides a clearcut interpretation of the two-mode squeezing mechanism in the de Sitter space. In addition, the curvature generated genuine tripartite entanglement is found to be less sensitive to the mass parameter than the generated bipartite entanglement. The effects of the curvature of de Sitter space on the generated entanglement become more apparent in the limit of conformal and massless scalar fields.
We study the distribution and generation of quantum coherence for two-mode and multi-mode Gaussian states in de Sitter space. It is found that the quantum coherence is redistributed among the mode in different open charts under the curvature effect of de Sitter space. In particular, the Gaussian coherence for the initially correlated state is found to survive in the limit of infinite curvature, while quantum entanglement vanishing in this limit. Unlike entanglement and steering, the coherence of a massive scalar field is more robust than a massless field under the influence of curvature of de Sitter space. In addition, it is shown that the curvature generates two-mode Gaussian state and three-mode Gaussian state quantum coherence among the open charts, even though the observers are localized in causally disconnected regions. It is worth noting that the gravity-generated three-mode coherence is extremely sensitive to the curvature effect for the conformal and massless scalar fields, which may be in principle employed to design an effective detector for the space curvature.
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a pure difference equation for the probability density by using the current conservation constraint. In the present study we observe some new features not seen in our previous approximate investigation, such as a nonzero minimum and maximum allowable size to the quantum universe: An examination of the effective classical dynamics supports the interpretation of a bouncing universe. The studied model suggests implications for the early universe, and plausibly also for the future of an ongoing accelerating phase of the universe.
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {it i.e.} $R times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.
Two important problems in studying the quantum black hole, namely the construction of the Hilbert space and the definition of the time evolution operator on such Hilbert space, are discussed using the de Sitter background field method for an observer far from the black hole. This is achieved through the ambient space formalism. Remarkably, in this approximation (distant observer), the theory preserves unitarity and analyticity, it is free from any infrared divergence, and it renders a quantum black hole entropy that turns out to be finite.
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