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arXiv:1612.02600 · Annals of Physics

Tripartite entanglement of fermionic system in accelerated frames

Salman Khan

Published Jun 9, 2014• 23 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2014.05.022

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arXiv:1103.0258•Mar 1, 2011•1 citation
The bipartite and tripartite entanglement of a 3-qubit fermionic system when one or two subsystems accelerate are investigated. It is shown that all the one-tangles decrease as the acceleration increases. However, unlike the scalar case, here one-tangles NCI(ABI){\mathcal{N}}_{{C}_{I}({\mathrm{AB}}_{I})}NCI​(ABI​)​ and NCI(AB){\mathcal{N}}_{{C}_{I}(\mathrm{AB})}NCI​(AB)​ never reduce to zero for any acceleration. It is found that the system has only tripartite entanglement when either one or two subsystems accelerate, which means that the acceleration does not generate bipartite entanglement and does not affect the entanglement structure of the quantum states in this system. It is of interest to note that the $\ensuremath{\pi}$-tangle of the two-observer-accelerated case decreases much quicker than that of the one-observer-accelerated case and it reduces to a nonzero minimum in the infinite-acceleration limit. Thus we argue that the qutrit systems are better than qubit systems in performing quantum information processing tasks in noninertial 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.