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arXiv:1103.0258

Tripartite Entanglements in Non-inertial Frames

Mahmoud Shamirzai, Esfahani, Bahram Nasr, Morteza Soltani

Published Mar 1, 2011• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1103.0258

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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.
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.
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.
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.
Abstract We investigate quantum entanglement and coherence of tripartite W state for Dirac fields under phase damping, phase flip and bit flip channels, respectively, in non-inertial frames. Via π -tangle, we numerically compute tripartite entanglement of W state under three channels when two observers are accelerated. We also analytically derive l 1 -norm quantum coherence of W state under the simultaneous influence of Unruh effect and noisy environments. For phase-damping and phase-flip channels, both the acceleration and noisy channels modulate the behaviour of the tripartitle entanglement and quantum coherence. They do not vanish even for infinite acceleration when only A 's qubit is under noisy environment, in contrast with the case when two or more observers’ qubits are under noisy environment. In the case of the bit flip channel, the behavior of the tripartite entanglement is similar to the one of the phase flip channel, but quantum coherence remains unaffected by the environment.
Abstract Using the single-mode approximation, we calculate entanglement measures such as negativity (1 − 3, 1 − 1 and 2 − 2 tangles) and von Neumann entropy for a tetrapartite Greenberger–Horne–Zeilinger system in a non-inertial frame. We then analyze the whole entanglement measures, the residual π 4 and geometric Π 4 average of tangles. We find that the difference between them is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer and others remaining stationary to all four accelerated observers. The results presented here show that entanglement still exists for the complete system even when acceleration r tends to infinity. The degree of entanglement is always equal to zero for the 1 − 1 tangle case. We also study the negativity 2 − 2 tangle for completeness. We reexamine the existence of the Unruh effect in non-inertial frames. It is also found that the von Neumann entropy increases with the increasing accelerated observers, and S κ I ζ I and S κ I ζ I δ I first increase and then decrease with the acceleration parameter r , e.g. S κ ζ ( max ) = 1.65853 at r = 0.599881 and S κ ζ δ ( max ) = 2.28231 at r = 0.676196. This implies that the subsystems ρ κ I ζ I and ρ κ I ζ I δ I are at first more disordered and then the disorder is reduced with the increasing acceleration parameter r .
Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state's distillable entanglement vanishes.