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arXiv:1012.4268 · Physical Review A

Multipartite entanglement of fermionic systems in noninertial frames

Jieci Wang, Jiliang Jing

Published Feb 17, 2011• 118 citations
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Abstract

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 ${\mathcal{N}}_{{C}_{I}({\mathrm{AB}}_{I})}$ and ${\mathcal{N}}_{{C}_{I}(\mathrm{AB})}$ 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.

DOI
10.1103/physreva.83.022314

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We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π 4 and Π 4 , are studied and illustrated with graphics through their dependence on the acceleration parameter r d for the first case and r c and r d for the second case. It is found that the negativities (1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter r d or in the second case r c and r d increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r > 0.472473 . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.

Chinese Physics B•Jul 1, 2019•17 citations
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 \ensuremathπ\ensuremath{\pi}\ensuremathπ-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.
We investigate the entanglement measures of tripartite W-State and GHZ-state in noninertial frame through the coordinate transformation between Minkowski and Rindler. First it is shown that all three qubits undergo in a uniform acceleration aaa of W-State, we find that the one-tangle, two-tangle, and πππ-tangle decrease when the acceleration parameter rrr increases, and the two-tangle cannot arrive to infinity of the acceleration. Next we show that the one qubit goes in a uniform acceleration a1a_{1}a1​ and the other two undergo in a uniform acceleration aaa of GHZ-state, we find that the two-tangle is equal to zero and NBI(AICI)=NCI(AIBI)≠NAI(BICI)N_{B_I (A_I C_I)} = N_{C_I (A_I B_I)}\neq N_{A_I (B_I C_I)}NBI​(AI​CI​)​=NCI​(AI​BI​)​=NAI​(BI​CI​)​, but one-tangle and πππ-tangle never reduce to zero for any acceleration.
In this work, we generalize the entanglement of three-qbit Bosonic systems beyond the single-mode approximation when one of the observers is accelerated. For this purpose, we review the effects of acceleration on field modes and quantum states. The single-mode approximation and beyond the single-mode approximation methods are introduced. After this brief introduction, the main problem of this paper, tripartite entanglement of bosonic systems in a noninertial frame beyond the single- mode approximation is investigated. The tripartite entangled states have different classes with GHZ and W states being most important. Here, we choose &pi-tangle as a measure of tripartite entanglement. If the three parties share GHZ state, the corresponding &pi-tangle will increase by increasing acceleration for some Unruh modes. This phenomenon, increasing entanglement, has never been observed in the single-mode approximation for bosonic case. Moreover, the &pi-tangle dose not exhibit a monotonic behavior with increasing acceleration. In the infinite acceleration limit, the &pi-tangle goes to different nonzero values for distinct Unruh modes. Unlike GHZ state, the entanglement of the W state shows only monotonically increasing and decreasing behaviors with increasing acceleration. Also, the entanglement for all possible choices of Unruh modes approaches only 0.176 in the high acceleration limit. Therefore, according to the quantum entanglement, there is no distinction between the single-mode approximation and beyond the single-mode approximation methods in this limit.
Based on Greenberger-Horne-Zeilinger (GHZGHZGHZ) and WWW initial states, the tripartite entanglement of a fermionic system under the amplitude damping channel and in depolarizing noise when two subsystems accelerated is investigated. Unlike the case of two-qubit system in which sudden death occurs easily, we find here that the sudden death never occurs even all subsystems are under the noise environment. We note that both acceleration and environment can destroy the symmetry between the subsystems, but the effect of environment is much stronger than that of acceleration. We also show that an entanglement rebound process will take place when P>0.75P>0.75P>0.75 in the depolarizing noise and the larger acceleration will result in the weaker rebound process.
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.
In this work we present the entanglement measures of a tripartite W-State entangled system in noninertial frame through the coordinate transformation between Minkowski and Rindler. Two cases are considered, i.e., when one qubit goes in a uniform acceleration a and the others remain stationary and when two qubits undergo in a uniform acceleration and while the other is stationary. The analytical negativities for one-tangle, two-tangle and π -tangle in total are not written out explicitly except for some special cases due to complicated expressions, but we illustrate them in graphics and study their dependencies on the acceleration parameters r b and r c . We find that the negativities of the one-tangle, two-tangle and π -tangle decrease with the acceleration parameters except for the constant N A B = N B A . The negativity N C I ( A B ) and the π C I decrease faster than N A ( B C I ) and π A ( π B ) . The negativities N A C I ( N B ( A C I ) )and N B I C I decrease faster than those N A B and N A B I , respectively. It is interesting to see there exist turning points for the negativity N A ( B I C I ) at the coordinate position ( r b , r c ) with r b = r c , which implies that the N A ( B I C I ) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem ρ A ( B I C I ) becomes smallest. The von Neumann entropy of tripartite system densities ρ A B C I and ρ A B I C I are obtained analytically. We notice that they all increase with the acceleration parameters r b and r c .
We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1–1 tangle, 1–3 tangle, and whole entanglement measurements π 4 and Π 4 , are studied and illustrated with graphics through their dependence on the acceleration parameter r d for the first case and r c and r d for the second case. It is found that the negativities (1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter r d or in the second case r c and r d increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when r > 0.472473 . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.