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Physical Review A

Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames

Wen-Chao Qiang, Guo-Hua Sun, Qian Dong, Shi‐Hai Dong

Published Aug 17, 2018• 96 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.98.022320

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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.
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.
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.
We investigate the geometric measure of quantum discord of all possible bipartite divisions of a tripartite system of Dirac fields in noninertial frames. As a comparison, we calculate the geometric measure of entanglement. We discuss the properties of geometric measure of quantum discord and geometric measure of entanglement for three qubit–qubit subsystems with acceleration parameter and the parameter describing the degree of entanglement the system in detail. We have found a conservative relationship involving two of three geometric discords in some condition and another conservative relationship involving three geometric discords for initially maximally entangled states. By the way, we also report some conservative relationships of concurrence, mutual information and geometric measure of entanglement for two bipartite subsystems.
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.
The monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the generalized concurrence. We show a monogamous equality involving the multipartite concurrence, all the bipartite concurrences, and the genuine tripartite entanglement for pure three-qubit systems. The result extends to mixed states in an inequality involving the generalized concurrence and all the bipartite concurrences. We provide a counterexample showing that the result cannot be extended for systems with more than three qubits.
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.