Quantum steering for continuous variable in de Sitter space
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Regular Article - Theoretical Physics
Quantum steering for continuous variable in de Sitter space Cuihong Wen, Jieci Wanga , Jiliang Jingb Department of Physics, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, Hunan, China
Received: 10 September 2019 / Accepted: 14 January 2020 © The Author(s) 2020
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.
1 Introduction Einstein–Podolsky–Rosen steering [1] captures the fact that one observer, can nonlocally manipulates, or steers, the state of the other subsystem by performing measurements on onehalf of an entangled state. Originally realized by Schrödinger [2,3], quantum steerability has been understood as a form of intermediate nonlocal correlation between Bell nonlocality and entanglement. It is recognized that steerability is an important resource for quite a few quantum information processing tasks, such as one-sided device-independent quantum key distribution [4,5] and subchannel discrimination [6]. In practice, different from the Bell tests, the demonstration of quantum steerability which is free of detection and locality loopholes is in reach [7], which make quantum steerability a ponderable concept in quantum information theory. For the foregoing reasons, quantum steerability has recently attracted increasing interest both from theoretical [8–17] and experimental [18–23] perspectives. Most recently, Tischler et.al reported an experimental demonstration of unidireca e-mail:
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tional steering, which is free either of the restrictions on the type of allowed measurements or of assumptions about the quantum state at hand [24]. 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 [25–34]. In particular, we know that any two mutually separated regions eventually become causally disconnected in the exponentially expanding de Sitter space. The Bogoliubov transformations between the open chart vacua and the Bunch–Davies vacuum which have support on both regions of a free massive scalar field were derived in [35]. Later, quantum correlations of scalar fields [36–39], Dirac fields [40] and axio
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