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Physica Scripta

Robustness of multipartite entangled states for fermionic systems under noisy channels in non-inertial frames

Kwang-Il Kim, Myong Chol Pak, Tae-Hyok Kim, Jong Chol Kim, Yong-Hae Ko, Hak Chol Pak

Published Dec 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ac437c

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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.
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 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.
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.
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.
Abstract Finding the most robust entangled states and the most fragile entangled states during the whole process of decoherence is particularly a fundamental problem for quantum physics and quantum information processing. Here the robustness of three‐qubit states under three different decoherence channels (amplitude damping, dephasing, bit flip) systematically are investigated, and the most robust genuine tripartite entangled states and the most fragile ones during each of the three decoherence processes are found. Moreover, the states with the most significant difference in robustness are shown to be locally unitarily equivalent to each other and therefore contain the same entanglement properties.