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arXiv:1507.00612 · Journal of High Energy Physics

Killing quantum entanglement by acceleration or a black hole

Yue Dai, Zhejun Shen, Yu Shi

Published Sep 1, 2015• 23 citations
arXivHTMLPDF

Abstract

We consider two entangled accelerating qubits coupled with real scalar fields, each described by the Unruh-Wald model. It is demonstrated that because of the Unruh effect of the fields, the bipartite entanglement between the two qubits suddenly dies when the acceleration of one or more qubits are large enough. We also consider three entangled accelerating qubits in GHZ state and in W state, with equal acceleration-frequency ratio, and found that in either state, the tripartite entanglement suddenly dies at a certain value of acceleration-frequency ratio. The equivalence between the Rindler metric and the Schwarzschild metric in the vicinity of the horizon of a black hole implies that for two entangled qubits outside a black hole, the entanglement suddenly dies when one or both of the qubits are close enough to the horizon, while the three entangled qubits in GHZ or W state, the tripartite entanglement suddenly dies when these qubits are close enough to the horizon.

DOI
10.1007/jhep09(2015)071

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We consider two entangled accelerating qubits coupled with real scalar fields, each described by the Unruh-Wald model. It is demonstrated that because of the Unruh effect of the fields, the bipartite entanglement between the two qubits suddenly dies when the acceleration of one or more qubits are large enough. We also consider three entangled accelerating qubits in GHZ state and in W state, with equal acceleration-frequency ratio, and found that in either state, the tripartite entanglement suddenly dies at a certain value of acceleration-frequency ratio. The equivalence between the Rindler metric and the Schwarzschild metric in the vicinity of the horizon of a black hole implies that for two entangled qubits outside a black hole, the entanglement suddenly dies when one or both of the qubits are close enough to the horizon, while the three entangled qubits in GHZ or W state, the tripartite entanglement suddenly dies when these qubits are close enough to the horizon.
We consider quantum entanglement of three accelerating qubits, each of which is locally coupled with a real scalar field, without causal influence among the qubits or among the fields. The initial states are assumed to be the GHZ and W states, which are the two representative three-partite entangled states. For each initial state, we study how various kinds of entanglement depend on the accelerations of the three qubits. All kinds of entanglement eventually suddenly die if at least two of three qubits have large enough accelerations. This result implies the eventual sudden death of all kinds of entanglement among three particles coupled with scalar fields when they are sufficiently close to the horizon of a black hole.
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.
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.
We use the Unruh effect to analyze the dynamics of classical and quantum correlations for a two-qubit system when one of them is uniformly accelerated for a finite amount of proper time. We show that the quantum correlation is completely destroyed in the limit of infinite acceleration, while the classical one remains nonzero. In particular, we show that such correlations exhibit the so-called sudden-change behavior as a function of acceleration. Eventually, we discuss how our results can be interpreted when the system lies in the vicinity of the event horizon of a Schwarzschild black hole.
We use the Unruh effect to investigate how the teleportation of quantum states is affected when one of the entangled qubits used in the process is under the influence of some external force. In order to reach a comprehensive understanding, a detailed analysis of the acceleration effect on such entangled qubit system is performed. In particular, we calculate the mutual information and concurrence between the two qubits and show that the latter has a ``sudden death'' at a finite acceleration, whose value will depend on the time interval along which the detector is accelerated.
The research subjects of information scrambling and the Unruh (anti-Unruh) effect are closely associated with black hole physics. We study the impact of acceleration on information scrambling under the Unruh (anti-Unruh) effect for two types of tripartite entangled states, namely the GHZ and W states. Our findings indicate that the anti-Unruh effect can result in stronger information scrambling, as measured by tripartite mutual information (TMI). Additionally, we show that the W state is more stable than the GHZ state under the influence of uniformly accelerated motion. Lastly, we extend our analysis to NNN-partite entangled states and product states.