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International Journal of Modern Physics B

Decoherence of GHZ state under three noisy channels in non-inertial frames

Kwang-Il Kim, Myong Chol Pak, Son A Kim, Jin Ju Ri, Tae-Hyok Kim

Published Jul 31, 2021• 2 citations
Publisher

Abstract

In this paper, we investigate the decoherence of GHZ state under three noisy channels in non-inertial frames. The phase flip, the bit flip and the phase damping channels are considered as noisy channels, respectively. By using three-tangle [Formula: see text] as the measurement of entanglement, we numerically calculate the genuine tripartite entanglement of GHZ state under noisy environments in non-inertial frames. Unlike the case of phase damping channel, in the cases of the phase flip and the bit flip ones, we find that the effect of environment cannot only decay the genuine tripartite entanglement, but also revive it.

DOI
10.1142/s021797922150209x

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In this paper, we investigate the decoherence of GHZ state under three noisy channels in non-inertial frames. The phase flip, the bit flip and the phase damping channels are considered as noisy channels, respectively. By using three-tangle [Formula: see text] as the measurement of entanglement, we numerically calculate the genuine tripartite entanglement of GHZ state under noisy environments in non-inertial frames. Unlike the case of phase damping channel, in the cases of the phase flip and the bit flip ones, we find that the effect of environment cannot only decay the genuine tripartite entanglement, but also revive it.
The one-tangle and π-tangle are used to quantify the entanglement of a tripartite Greenberger–Horne–Zeilinger (GHZ) state in non-inertial frames when the system interacts with a noisy environment in the form of phase damping, phase flip and bit flip channels. It is shown that the two-tangles behave as a closed system. The one-tangle and π-tangle have different behaviors in the three channels. In the case of the phase damping channel, depending on the kind of coupling, the sudden death of both the one-tangle and π-tangle may or may not happen, whereas in the case of the phase flip channel the sudden death cannot be avoided. The effect of decoherence may be ignored in the limit of infinite acceleration when the system interacts with a bit flip channel. Furthermore, a sudden rebirth of the one-tangle and π-tangle occurs in the case of the phase flip channel which may be delayed when collective coupling is switched on.
Abstract We investigate robustness of bipartite and tripartite entangled states for fermionic systems in non-inertial frames, which are under noisy channels. We consider two Bell states and two Greenberger-Horne-Zeilinger (GHZ) states, which possess initially the same amount of entanglement, respectively. By using genuine multipartite (GM) concurrence, we analytically derive the equations that determine the difference between the robustness of these locally unitarily equivalent states under the amplitude-damping channel. We find that tendency of the robustness for two GHZ states evaluated by using three-tangle τ and GM concurrence as measures of genuine tripartite entanglement is equal to each other. We also find that the robustness of two Bell states is equal to each other under the depolarizing, phase damping and bit flip channels, and that the same is true for two GHZ states.
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.
The decoherence effect on multipartite entanglement in non-inertial frames is investigated. The GHZ state is considered to be shared between partners with one partner in the inertial frame whereas the other two are in accelerated frames. One-tangle and π-tangles are used to quantify the entanglement of the multipartite system influenced by phase damping and phase flip channels. It is seen that for the phase damping channel, entanglement sudden death (ESD) occurs for p > 0.5 in the infinite acceleration limit. On the other hand, in the case of the phase flip channel, ESD behavior occurs at p = 0.5. It is also seen that entanglement sudden birth (ESB) occurs in the case of phase flip channel just after ESD, i.e. p > 0.5. Furthermore, it is seen that the effect of the environment on multipartite entanglement is much stronger than that of the acceleration of non-inertial frames.
In this paper, we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment, and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames. Through the calculations and analyses, it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel, while the system is under the phase damping and flip channels. This protection protocol cannot prevent entanglement but will accelerate the death of entanglement. In addition, if the system is in the noninertial reference frame, then the effect of weak measurement will be weakened for the amplitude damping channel. Nevertheless, for other decoherence channels, the Unruh effect does not affect the quantum weak measurement, the only exception is that the maximum value of entanglement is reduced to √2/2 of the original value in the inertial frames.
Ardehali (Phys. Rev. A, 46, 5375 (1992). 10.1103/PhysRevA.46.5375 ) derived a Bell-type inequality for an n-particle system in a Greenberger–Horne–Zeilinger (GHZ) state. This inequality helps relax the detection efficiencies required for closing the detection loophole in Bell tests. Coffman et al. (Phys. Rev. A, 61, 052306 (2000). doi: 10.1103/PhysRevA.61.052306 ) gave a simplified form of tripartite entanglement of three-qubit pure states. We use theory and experiment to investigate both results using three-qubit GHZ states with different intensities of bit-flip noise. The purpose of our work is to relate the Ardehali inequality and the tripartite concurrence of the tripartite GHZ states in a noisy environment. Our results show that the experimental values are quite consistent with theoretical predictions for three-qubit GHZ states in a bit-flip noisy environment.