Abstract
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. It is found 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.
Highlights
On the other hand, it is of great interest to study the behavior of quantum entanglement and other quantum correlations for discrete variables between causally disconnected regions in the context of cosmology [25,26,27,28,29,30,31,32,33,34]
Bob and antiBob can steer each other when the curvature is strong enough even though they are separated by the event horizon, which verifies the fact that the quantum steerability is one kind of nonlocal quantum correlation
We have studied the distribution of steerability among the mode A(B) described by Alice (Bob) in the de Sitter region R, and the complimentary mode Bdescribed by a hypothetical observer anti-Bob in the causally disconnected region L
Summary
It is of great interest to study the behavior of quantum entanglement and other quantum correlations for discrete variables between causally disconnected regions in the context of cosmology [25,26,27,28,29,30,31,32,33,34]. Quantum correlations of scalar fields [36,37,38,39], Dirac fields [40] and axion fields [41,42] were studied in de Sitter space. In [43,44], the authors studied the observable effect of quantum information on the cosmic microwave background since there are some entanglement between causally separated regions in de Sitter space. It is important to study the quantum steering between causally disconnected regions of de Sitter space because one can never communicate classically between them. We will derive the phase-space description of quantum state evolution for continuous variables basing on the Bogoliubov transformation between the open chart vacua and the Bunch–Davies vacuum. It is found that the quantum steerability between Alice and Bob is apparently affected by the curvature of de Sitter space when the mass parameter ν approaches to the
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