Abstract We study the impact of acceleration on information delocalization 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 delocalization of quantum information, 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 N-partite entangled states and product states.
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
W state initially, the corresponding $\ensuremath{\pi}$-tangle, one of the measures of tripartite entanglement, is shown to be $\ensuremath{\pi}/6~0.524$ or
0.176 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.
Abstract We study the acceleration effect on the genuine tripartite entanglement for one or two accelerated detector(s) coupled to the vacuum field. Surprisingly, we find that the increase and decrease in entanglement have no definite correspondence with the Unruh and anti-Unruh effects. Specifically, Unruh effect can not only decrease but also enhance the tripartite entanglement between detectors; also, anti-Unruh effect can not only enhance but also decrease the tripartite entanglement. We give an explanation of this phenomenon. Finally, we extend the discussion from tripartite to N-partite systems.
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 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.
The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single-mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence. First we investigate tripartite systems, considering both GHZ and
W states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a nonzero value. These results hold for both single- and two-qubit acceleration. In the GHZ and
W states the coherence is distributed as correlations between the qubits and is known as global coherence. However, quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate a separable state. The GHZ state,
W state, and separable states contain only one type of coherence. Next we consider the
WW and star states in which both local and global coherences coexist. We find that under uniform acceleration both local and global coherence show similar qualitative behavior. Finally, we derive analytic expressions for the quantum coherence of
N-partite GHZ and
W states for
n<N accelerating qubits. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite
W states the quantum coherence decreases only polynomially. We conclude that
W states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black-hole physics.