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arXiv:quant-ph/0603269 · Physical Review A

Entanglement of Dirac fields in noninertial frames

Paul M. Alsing, Ivette Fuentes, Robert B. Mann, Tracey E. Tessier

Published Sep 20, 2006• 483 citations
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Abstract

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.

DOI
10.1103/physreva.74.032326

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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.
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.
Quantum entanglement is foundational to quantum computation. Yet little is known about how this phenomenon is modified by gravitational effects. One place to begin this study is by consideration of observers in relative acceleration. Here I describe recent work exploring the relationship between quantum entanglement between states shared by such observers. Due to the Unruh effect, the entanglement is degraded and asymptotically reaches a minimum value in the infinite acceleration limit. For bosons this value is zero, but for fermions it is nonzero, in which case quantum information tasks such as teleportation between parties in relative uniform acceleration can always be performed. I discuss the implications of these results for observers in gravitational fields. © 2008 Physics Essay Publications. DOI: XXXX Resume: L’enchevetrement quantique est fondamentale pour le calcul quantique. Pourtant tres peu est connu a propos de comment ce phenomene est modifie par les effets gravitationnels. Une maniere d’entamer cette etude est de considerer des observateurs en acceleration relative. Ici je decris des travaux recents qui explore les relations entre enchevetrement quantique d’etats partages par de tels observateurs. A cause de l’effet dit de Unruh, cet enchevetrement est degrade et atteint asymptotiquement une valeur minimum dans la limite d’une acceleration infinie. Pour les bosons cette valeur est nulle, alors que pour des fermions cette valeur est non zero. Dans ce cas, les operations d’informations quantiques tel que la teleportation entre differentes parties en acceleration relatives peuvent toujours etre etre implementees. Je discusse les implications de ces resultats pour des observateurs dans un champ gravitationel.
We apply genuine multipartite entanglement concurrence to investigate entanglement properties of Dirac fields in noninertial frames. We present analytical concurrences for bipartite and tripartite entanglements simultaneously, which enriches previous results. We note that the entanglement of the Greenberger-Horne-Zeilinger-like state is degraded by the Unruh effect, but this entangled system always remains entangled to a degree and can be used in quantum teleportation between parties in relatively uniform acceleration. We find that all tripartite subsystems in noninertial frames are monogamous in that they all satisfy Coffmann-Kundu-Wootters monogamous inequality. We also find two useful relations regarding concurrences.
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.
Quantum coherence as the fundamental characteristic of quantum physics, provides the valuable resource for quantum computation in exceeding the power of classical algorithms. The exploration of quantum coherence in relativistic systems is of significance from both the fundamental points of view and practical applications. We investigate the quantum coherence of two free modes of scalar and Dirac fields as detected by two relatively accelerated observers by resorting to the relative entropy of coherence. We show that the relative entropy of coherence monotonically decreases when acceleration goes up, as a consequence of the Unruh effect. Specifically, the initial states with parameters α=bα=bα=b and α=1−b2α=\sqrt{1-b^2}α=1−b2​ have the same initial relative entropy coherence at a=0a=0a=0 (with aaa the acceleration), but degrade along two different trajectories. The relative entropy of coherence reaches vanishing value in the scalar field in the infinite acceleration limit, but non-vanishing value in the Dirac field. This suggests that in the Dirac field, the bipartite state possesses quantum coherence to some extent with the variation of the relative acceleration, and may lead to potential applications in quantum computation performed by observers in motion relatively.
The entanglement between two modes of a free scalar field (or a free Dirac field) is investigated in noninertial frames under the condition that they are initially prepared in a Werner state. It is found that the entanglement degradation induced by the Unruh effect highly depends on the initial purity f and the type of fields. For a fixed acceleration r , the critical values of f for the states entangled or separable are obtained in both scalar and Dirac fields. Finally, we make a comparison between the entanglement and the quantum discord and show that quantum discord is more robust than entanglement in our models.