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arXiv:quant-ph/0410172 · Physical Review Letters

Alice Falls into a Black Hole: Entanglement in Noninertial Frames

Ivette Fuentes, Robert B. Mann

Published Sep 14, 2005• 599 citations
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Abstract

Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state's distillable entanglement vanishes.

DOI
10.1103/physrevlett.95.120404

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•Sep 19, 2008•1 citation
Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state's distillable entanglement vanishes.
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.
The entanglement between two modes of free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\ensuremath{\alpha}$ and its ``normalized partner'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\ensuremath{\alpha}$ for the scalar field, but always remains entangled to a degree that is dependent on $\ensuremath{\alpha}$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\ensuremath{\alpha}$ and the type of field.
We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.
Entanglement degradation caused by the Unruh effect is discussed for the tripartite GHZ or W states constructed by modes of a non-interacting quantum field viewed by one inertial observer and two uniformly accelerated observers. For fermionic states, the Unruh effect even for infinite accelerations cannot completely remove the entanglement. However, for the bosonic states, the situation is different and the entanglement vanishes asymptotically. Also, the entanglement is studied for the bipartite subsystems. While for the GHZ states all the bipartite subsystems are identically disentangled, for the W states the bipartite subsystems are somewhat entangled, though, this entanglement can be removed for appropriately accelerated observers. Interestingly, logarithmic negativity as a measure for determining the entanglement of one part of the system relative to the other two parts, is not generally the same for different parts. This means that we encounter tripartite systems where each part is differently entangled to the other two parts.
Tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As the Unruh effect indicates, tripartite entanglement exhibits a decreasing behavior with increasing acceleration. Unlike bipartite entanglement, however, tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or WWW state initially, the corresponding $\ensuremath{\pi}$-tangle, one of the measures of tripartite entanglement, is shown to be $\ensuremath{\pi}/6~0.524$ or 0.1760.1760.176 in this limit, respectively. This fact indicates that tripartite quantum-information processing may be possible even if one of the parties approaches the Rindler horizon. The physical implications of this striking result are discussed in the context of black-hole physics.
This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. \n \nIt is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. \n \nThe dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.